Skocz do pozycji: 1.

Tytuł:

4-Transitive Digraphs I: The Structure of Strong 4-Transitive Digraphs

Autorzy:

Hernández-Cruz, César

Powiązania:

https://bibliotekanauki.pl/articles/30146649.pdf

Data publikacji:

2013-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
transitive digraph
quasi-transitive digraph
4-transitive digraph
k-transitive digraph
k-quasi-transitive digraph

Opis:

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is transitive if for every three distinct vertices u, v,w ∈ V (D), (u, v), (v,w) ∈ A(D) implies that (u,w) ∈ A(D). This concept can be generalized as follows: A digraph is k-transitive if for every u, v ∈ V (D), the existence of a uv-directed path of length k in D implies that (u, v) ∈ A(D). A very useful structural characterization of transitive digraphs has been known for a long time, and recently, 3-transitive digraphs have been characterized. In this work, some general structural results are proved for k-transitive digraphs with arbitrary k ≥ 2. Some of this results are used to characterize the family of 4-transitive digraphs. Also some of the general results remain valid for k-quasi-transitive digraphs considering an additional hypothesis. A conjecture on a structural property of k-transitive digraphs is proposed.

Źródło:

Discussiones Mathematicae Graph Theory; 2013, 33, 2; 247-260
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:

k-kernels in generalizations of transitive digraphs

Autorzy:

Galeana-Sánchez, Hortensia
Hernández-Cruz, César

Powiązania:

https://bibliotekanauki.pl/articles/743887.pdf

Data publikacji:

2011

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
kernel
(k,l)-kernel
k-kernel
transitive digraph
quasi-transitive digraph
right-pretransitive digraph
left-pretransitive digraph
pretransitive digraph

Opis:

Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively.
A (k,l)-kernel N of D is a k-independent set of vertices (if u,v ∈ N, u ≠ v, then d(u,v), d(v,u) ≥ k) and l-absorbent (if u ∈ V(D)-N then there exists v ∈ N such that d(u,v) ≤ l). A k-kernel is a (k,k-1)-kernel. Quasi-transitive, right-pretransitive and left-pretransitive digraphs are generalizations of transitive digraphs. In this paper the following results are proved: Let D be a right-(left-) pretransitive strong digraph such that every directed triangle of D is symmetrical, then D has a k-kernel for every integer k ≥ 3; the result is also valid for non-strong digraphs in the right-pretransitive case. We also give a proof of the fact that every quasi-transitive digraph has a (k,l)-kernel for every integers k > l ≥ 3 or k = 3 and l = 2.

Źródło:

Discussiones Mathematicae Graph Theory; 2011, 31, 2; 293-312
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:

3-transitive digraphs

Autorzy:

Hernández-Cruz, César

Powiązania:

https://bibliotekanauki.pl/articles/743218.pdf

Data publikacji:

2012

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
kernel
transitive digraph
quasi-transitive digraph
3-transitive digraph
3-quasi-transitive digraph

Opis:

Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively. A digraph D is 3-transitive if the existence of the directed path (u,v,w,x) of length 3 in D implies the existence of the arc (u,x) ∈ A(D). In this article strong 3-transitive digraphs are characterized and the structure of non-strong 3-transitive digraphs is described. The results are used, e.g., to characterize 3-transitive digraphs that are transitive and to characterize 3-transitive digraphs with a kernel.

Źródło:

Discussiones Mathematicae Graph Theory; 2012, 32, 2; 205-219
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 4.

Tytuł:

Radii and centers in iterated line digraphs

Autorzy:

Knor, Martin
Niepel, L'udovít

Powiązania:

https://bibliotekanauki.pl/articles/972028.pdf

Data publikacji:

1996

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

center
digraph
line digraph
radius

Opis:

We show that the out-radius and the radius grow linearly, or "almost" linearly, in iterated line digraphs. Further, iterated line digraphs with a prescribed out-center, or a center, are constructed. It is shown that not every line digraph is admissible as an out-center of line digraph.

Źródło:

Discussiones Mathematicae Graph Theory; 1996, 16, 1; 17-26
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 5.

Tytuł:

(K − 1)-Kernels In Strong K-Transitive Digraphs

Autorzy:

Wang, Ruixia

Powiązania:

https://bibliotekanauki.pl/articles/31339493.pdf

Data publikacji:

2015-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
transitive digraph
k-transitive digraph
k-kernel

Opis:

Let D = (V (D),A(D)) be a digraph and k ≥ 2 be an integer. A subset N of V (D) is k-independent if for every pair of vertices u, v ∈ N, we have d(u, v) ≥ k; it is l-absorbent if for every u ∈ V (D) − N, there exists v ∈ N such that d(u, v) ≤ l. A (k, l)-kernel of D is a k-independent and l-absorbent subset of V (D). A k-kernel is a (k, k − 1)-kernel. A digraph D is k-transitive if for any path x₀x₁・・・ x_k of length k, x₀ dominates x_k. Hernández-Cruz [3-transitive digraphs, Discuss. Math. Graph Theory 32 (2012) 205-219] proved that a 3-transitive digraph has a 2-kernel if and only if it has no terminal strong component isomorphic to a 3-cycle. In this paper, we generalize the result to strong k-transitive digraphs and prove that a strong k-transitive digraph with k ≥ 4 has a (k − 1)-kernel if and only if it is not isomorphic to a k-cycle.

Źródło:

Discussiones Mathematicae Graph Theory; 2015, 35, 2; 229-235
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 6.

Tytuł:

Some remarks on the structure of strong $k$-transitive digraphs

Autorzy:

Hernández-Cruz, César
Montellano-Ballesteros, Juan José

Powiązania:

https://bibliotekanauki.pl/articles/30148710.pdf

Data publikacji:

2014-11-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
transitive digraph
k-transitive digraph
quasi-transitive digraph
k-quasi-transitive digraph
Laborde-Payan-Xuong Conjecture

Opis:

A digraph $D$ is $k$-transitive if the existence of a directed path ($v_0, v_1, . . ., v_k$), of length $k$ implies that ($v_0, v_k) ∈ A(D)$. Clearly, a 2-transitive digraph is a transitive digraph in the usual sense. Transitive digraphs have been characterized as compositions of complete digraphs on an acyclic transitive digraph. Also, strong 3 and 4-transitive digraphs have been characterized. In this work we analyze the structure of strong $k$-transitive digraphs having a cycle of length at least $k$. We show that in most cases, such digraphs are complete digraphs or cycle extensions. Also, the obtained results are used to prove some particular cases of the Laborde-Payan-Xuong Conjecture.

Źródło:

Discussiones Mathematicae Graph Theory; 2014, 34, 4; 651-671
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 7.

Tytuł:

A note on kernels and solutions in digraphs

Autorzy:

Harminc, Matúš
Soták, Roman

Powiązania:

https://bibliotekanauki.pl/articles/744158.pdf

Data publikacji:

1999

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

kernel of digraph
solution of digraph

Opis:

For given nonnegative integers k,s an upper bound on the minimum number of vertices of a strongly connected digraph with exactly k kernels and s solutions is presented.

Źródło:

Discussiones Mathematicae Graph Theory; 1999, 19, 2; 237-240
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 8.

Tytuł:

Kernels by Monochromatic Paths and Color-Perfect Digraphs

Autorzy:

Galeana-Śanchez, Hortensia
Sánchez-López, Rocío

Powiązania:

https://bibliotekanauki.pl/articles/31340961.pdf

Data publikacji:

2016-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

kernel
kernel perfect digraph
kernel by monochromatic paths
color-class digraph
quasi color-perfect digraph
color-perfect digraph

Opis:

For a digraph D, V (D) and A(D) will denote the sets of vertices and arcs of D respectively. In an arc-colored digraph, a subset K of V(D) is said to be kernel by monochromatic paths (mp-kernel) if (1) for any two different vertices x, y in N there is no monochromatic directed path between them (N is mp-independent) and (2) for each vertex u in V (D) \ N there exists v ∈ N such that there is a monochromatic directed path from u to v in D (N is mp-absorbent). If every arc in D has a different color, then a kernel by monochromatic paths is said to be a kernel. Two associated digraphs to an arc-colored digraph are the closure and the color-class digraph _C(D). In this paper we will approach an mp-kernel via the closure of induced subdigraphs of D which have the property of having few colors in their arcs with respect to D. We will introduce the concept of color-perfect digraph and we are going to prove that if D is an arc-colored digraph such that D is a quasi color-perfect digraph and _C(D) is not strong, then D has an mp-kernel. Previous interesting results are generalized, as for example Richardson′s Theorem.

Źródło:

Discussiones Mathematicae Graph Theory; 2016, 36, 2; 309-321
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 9.

Tytuł:

k-Kernels and some operations in digraphs

Autorzy:

Galeana-Sanchez, Hortensia
Pastrana, Laura

Powiązania:

https://bibliotekanauki.pl/articles/743109.pdf

Data publikacji:

2009

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

k-kernel
k-subdivision digraph
k-middle digraph and k-total digraph

Opis:

Let D be a digraph. V(D) denotes the set of vertices of D; a set N ⊆ V(D) is said to be a k-kernel of D if it satisfies the following two conditions: for every pair of different vertices u,v ∈ N it holds that every directed path between them has length at least k and for every vertex x ∈ V(D)-N there is a vertex y ∈ N such that there is an xy-directed path of length at most k-1. In this paper, we consider some operations on digraphs and prove the existence of k-kernels in digraphs formed by these operations from another digraphs.

Źródło:

Discussiones Mathematicae Graph Theory; 2009, 29, 1; 39-49
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 10.

Tytuł:

On graphs all of whose {C₃,T₃}-free arc colorations are kernel-perfect

Autorzy:

Galeana-Sánchez, Hortensia
García-Ruvalcaba, José

Powiązania:

https://bibliotekanauki.pl/articles/743429.pdf

Data publikacji:

2001

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

kernel
kernel-perfect digraph
m-coloured digraph

Opis:

A digraph D is called a kernel-perfect digraph or KP-digraph when every induced subdigraph of D has a kernel.
We call the digraph D an m-coloured digraph if the arcs of D are coloured with m distinct colours. A path P is monochromatic in D if all of its arcs are coloured alike in D. The closure of D, denoted by ζ(D), is the m-coloured digraph defined as follows:
V( ζ(D)) = V(D), and
A( ζ(D)) = ∪_{i} {(u,v) with colour i: there exists a monochromatic path of colour i from the vertex u to the vertex v contained in D}.
We will denoted by T₃ and C₃, the transitive tournament of order 3 and the 3-directed-cycle respectively; both of whose arcs are coloured with three different colours.
Let G be a simple graph. By an m-orientation-coloration of G we mean an m-coloured digraph which is an asymmetric orientation of G.
By the class E we mean the set of all the simple graphs G that for any m-orientation-coloration D without C₃ or T₃, we have that ζ(D) is a KP-digraph.
In this paper we prove that if G is a hamiltonian graph of class E, then its complement has at most one nontrivial component, and this component is K₃ or a star.

Źródło:

Discussiones Mathematicae Graph Theory; 2001, 21, 1; 77-93
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 11.

Tytuł:

On the Optimality of 3-Restricted Arc Connectivity for Digraphs and Bipartite Digraphs

Autorzy:

Zhang, Yaoyao
Meng, Jixiang

Powiązania:

https://bibliotekanauki.pl/articles/32361733.pdf

Data publikacji:

2022-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

restricted arc-connectivity
bipartite digraph
optimality
digraph
network

Opis:

Let D be a strong digraph. An arc subset S is a k-restricted arc cut of D if D − S has a strong component D′ with order at least k such that D\V (D′) contains a connected subdigraph with order at least k. If such a k-restricted arc cut exists in D, then D is called λ^k-connected. For a λ^k-connected digraph D, the k-restricted arc connectivity, denoted by λ^k(D), is the minimum cardinality over all k-restricted arc cuts of D. It is known that for many digraphs λ^k(D) ≤ ξ^k(D), where ξ^k(D) denotes the minimum k-degree of D. D is called λ^k-optimal if λ^k(D) = ξ^k(D). In this paper, we will give some sufficient conditions for digraphs and bipartite digraphs to be λ³-optimal.

Źródło:

Discussiones Mathematicae Graph Theory; 2022, 42, 2; 321-332
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

Artykuł

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Skocz do pozycji: 12.

Tytuł:

Kernels in monochromatic path digraphs

Autorzy:

Galeana-Sánchez, Hortensia
Ramírez, Laura
Mejía, Hugo

Powiązania:

https://bibliotekanauki.pl/articles/744174.pdf

Data publikacji:

2005

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

kernel
line digraph
kernel by monochromatic paths
monochromatic path digraph
edge-coloured digraph

Opis:

We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. Let D be an m-coloured digraph. A set N ⊆ V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions:
(i) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them and
(ii) for each vertex x ∈ (V(D)-N) there is a vertex y ∈ N such that there is an xy-monochromatic directed path.
In this paper is defined the monochromatic path digraph of D, MP(D), and the inner m-colouration of MP(D). Also it is proved that if D is an m-coloured digraph without monochromatic directed cycles, then the number of kernels by monochromatic paths in D is equal to the number of kernels by monochromatic paths in the inner m-colouration of MP(D). A previous result is generalized.

Źródło:

Discussiones Mathematicae Graph Theory; 2005, 25, 3; 407-417
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 13.

Tytuł:

Monochromatic paths and monochromatic sets of arcs in 3-quasitransitive digraphs

Autorzy:

Galeana-Sánchez, Hortensia
Rojas-Monroy, R.
Zavala, B.

Powiązania:

https://bibliotekanauki.pl/articles/744398.pdf

Data publikacji:

2009

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

m-coloured digraph
3-quasitransitive digraph
kernel by monochromatic paths
γ-cycle
quasi-monochromatic digraph

Opis:

We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path is called monochromatic if all of its arcs are coloured alike. A set N of vertices of D is called a kernel by monochromatic paths if for every pair of vertices of N there is no monochromatic path between them and for every vertex v ∉ N there is a monochromatic path from v to N. We denote by A⁺(u) the set of arcs of D that have u as the initial vertex. We prove that if D is an m-coloured 3-quasitransitive digraph such that for every vertex u of D, A⁺(u) is monochromatic and D satisfies some colouring conditions over one subdigraph of D of order 3 and two subdigraphs of D of order 4, then D has a kernel by monochromatic paths.

Źródło:

Discussiones Mathematicae Graph Theory; 2009, 29, 2; 337-347
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 14.

Tytuł:

Underlying Graphs of 3-Quasi-Transitive Digraphs and 3-Transitive Digraphs

Autorzy:

Wang, Ruixia
Wang, Shiying

Powiązania:

https://bibliotekanauki.pl/articles/30146536.pdf

Data publikacji:

2013-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

graph orientation
3-quasi-transitive digraph
3-transitive digraph

Opis:

A digraph is 3-quasi-transitive (resp. 3-transitive), if for any path x₀x₁ x₂x₃ of length 3, x₀ and x₃ are adjacent (resp. x₀ dominates x₃). César Hernández-Cruz conjectured that if D is a 3-quasi-transitive digraph, then the underlying graph of D, UG(D), admits a 3-transitive orientation. In this paper, we shall prove that the conjecture is true.

Źródło:

Discussiones Mathematicae Graph Theory; 2013, 33, 2; 429-435
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 15.

Tytuł:

Hamiltonian Cycle Problem in Strong k-Quasi-Transitive Digraphs with Large Diameter

Autorzy:

Wang, Ruixia

Powiązania:

https://bibliotekanauki.pl/articles/32083906.pdf

Data publikacji:

2021-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

quasi-transitive digraph
k -quasi-transitive digraph
Hamiltonian cycle

Opis:

Let k be an integer with k ≥ 2. A digraph is k-quasi-transitive, if for any path x₀x₁... x_k of length k, x₀ and x_k are adjacent. Let D be a strong k-quasi-transitive digraph with even k ≥ 4 and diameter at least k +2. It has been shown that D has a Hamiltonian path. However, the Hamiltonian cycle problem in D is still open. In this paper, we shall show that D may contain no Hamiltonian cycle with k ≥ 6 and give the sufficient condition for D to be Hamiltonian.

Źródło:

Discussiones Mathematicae Graph Theory; 2021, 41, 2; 685-690
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

Artykuł

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Skocz do pozycji: 16.

Tytuł:

Kernels in edge coloured line digraph

Autorzy:

Galeana-Sánchez, H.
Pastrana Ramírez, L.

Powiązania:

https://bibliotekanauki.pl/articles/744205.pdf

Data publikacji:

1998

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

kernel
kernel by monochromatic paths
line digraph
edge coloured digraph

Opis:

We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. A set N ⊆ V(D) is said to be a kernel by monochromatic paths if it satisfies the two following conditions (i) for every pair of different vertices u, v ∈ N there is no monochromatic directed path between them and (ii) for every vertex x ∈ V(D)-N there is a vertex y ∈ N such that there is an xy-monochromatic directed path.
Let D be an m-coloured digraph and L(D) its line digraph. The inner m-coloration of L(D) is the edge coloration of L(D) defined as follows: If h is an arc of D of colour c, then any arc of the form (x,h) in L(D) also has colour c.
In this paper it is proved that if D is an m-coloured digraph without monochromatic directed cycles, then the number of kernels by monochromatic paths in D is equal to the number of kernels by monochromatic paths in the inner edge coloration of L(D).

Źródło:

Discussiones Mathematicae Graph Theory; 1998, 18, 1; 91-98
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 17.

Tytuł:

On arc-coloring of digraphs

Autorzy:

Zwonek, M.

Powiązania:

https://bibliotekanauki.pl/articles/254973.pdf

Data publikacji:

2006

Wydawca:

Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH

Tematy:

arc-coloring
digraph

Opis:

In the paper we deal with the problem of the arc-colouring of some classes of digraphs (tournaments, complete digraphs and products of digraphs).

Źródło:

Opuscula Mathematica; 2006, 26, 1; 185-195
1232-9274
2300-6919

Pojawia się w:

Opuscula Mathematica

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 18.

Tytuł:

Toward Wojdas conjecture on digraph packing

Autorzy:

Konarski, J.
Żak, A.

Powiązania:

https://bibliotekanauki.pl/articles/255123.pdf

Data publikacji:

2017

Wydawca:

Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH

Tematy:

packing
digraph
size

Opis:

Given a positive integer m ≤ n/2, Wojda conjectured in 1985 that if D1 and D2 are digraphs of order n such that [formula] and [formula] then D1 and D2 pack. The cases when m = 1 or m = n/2 follow from known results. Here we prove the conjecture for [formula].

Źródło:

Opuscula Mathematica; 2017, 37, 4; 589-595
1232-9274
2300-6919

Pojawia się w:

Opuscula Mathematica

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 19.

Tytuł:

The spectrum problem for digraphs of order 4 and size 5

Autorzy:

Bunge, R. C.
DeShong, S,
El-Zanati, S. I.
Fischer, A.
Roberts, D. P.
Teng, L.

Powiązania:

https://bibliotekanauki.pl/articles/255132.pdf

Data publikacji:

2018

Wydawca:

Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH

Tematy:

spectrum problem
digraph decompositions

Opis:

The paw graph consists of a triangle with a pendant edge attached to one of the three vertices. We obtain a multigraph by adding exactly one repeated edge to the paw. Now, let D be a directed graph obtained by orientating the edges of that multigraph. For 12 of the 18 possibilities for D, we establish necessary and sufficient conditions on n for the existence of a [formula] design. Partial results are given for the remaining 6 possibilities for D.

Źródło:

Opuscula Mathematica; 2018, 38, 1; 15-30
1232-9274
2300-6919

Pojawia się w:

Opuscula Mathematica

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 20.

Tytuł:

A Sokoban-type game and arc deletion within irregular digraphs of all sizes

Autorzy:

Dziechcińska-Halamoda, Zyta
Majcher, Zofia
Skupień, Zdzisław

Powiązania:

https://bibliotekanauki.pl/articles/743481.pdf

Data publikacji:

2007

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

irregular digraph
all sizes

Opis:

Digraphs in which ordered pairs of out- and in-degrees of vertices are mutually distinct are called irregular, see Gargano et al. [3]. Our investigations focus on the problem: what are possible sizes of irregular digraphs (oriented graphs) for a given order n? We show that those sizes in both cases make up integer intervals. The extremal sizes (the endpoints of these intervals) are found in [1,5]. In this paper we construct, with help of Sokoban-type game, n-vertex irregular oriented graphs (irregular digraphs) of all intermediate sizes.

Źródło:

Discussiones Mathematicae Graph Theory; 2007, 27, 3; 611-622
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 21.

Tytuł:

A sufficient condition for the existence of k-kernels in digraphs

Autorzy:

Galeana-Sánchez, H.
Rincón-Mejía, H.

Powiązania:

https://bibliotekanauki.pl/articles/744223.pdf

Data publikacji:

1998

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
kernel
k-kernel

Opis:

In this paper, we prove the following sufficient condition for the existence of k-kernels in digraphs: Let D be a digraph whose asymmetrical part is strongly conneted and such that every directed triangle has at least two symmetrical arcs. If every directed cycle γ of D with l(γ) ≢ 0 (mod k), k ≥ 2 satisfies at least one of the following properties: (a) γ has two symmetrical arcs, (b) γ has four short chords. Then D has a k-kernel.
This result generalizes some previous results on the existence of kernels and k-kernels in digraphs. In particular, it generalizes the following Theorem of M. Kwaśnik [5]: Let D be a strongly connected digraph, if every directed cycle of D has length ≡ 0 (mod k), k ≥ 2. Then D has a k-kernel.

Źródło:

Discussiones Mathematicae Graph Theory; 1998, 18, 2; 197-204
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 22.

Tytuł:

Sufficient Conditions for a Digraph to Admit A (1, ≤ ℓ)-Identifying Code

Autorzy:

Balbuena, Camino
Dalfó, Cristina
Martínez-Barona, Berenice

Powiązania:

https://bibliotekanauki.pl/articles/32222715.pdf

Data publikacji:

2021-11-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

graph
digraph
identifying code

Opis:

A (1, ≤ ℓ)-identifying code in a digraph D is a subset C of vertices of D such that all distinct subsets of vertices of cardinality at most ℓ have distinct closed in-neighbourhoods within C. In this paper, we give some sufficient conditions for a digraph of minimum in-degree δ⁻ ≥ 1 to admit a (1, ≤ ℓ)-identifying code for ℓ ∈ {δ⁻, δ⁻ + 1}. As a corollary, we obtain the result by Laihonen that states that a graph of minimum degree δ ≥ 2 and girth at least 7 admits a (1, ≤ δ)-identifying code. Moreover, we prove that every 1-in-regular digraph has a (1, ≤ 2)-identifying code if and only if the girth of the digraph is at least 5. We also characterize all the 2-in-regular digraphs admitting a (1, ≤ ℓ)-identifying code for ℓ ∈ {2, 3}.

Źródło:

Discussiones Mathematicae Graph Theory; 2021, 41, 4; 853-872
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 23.

Tytuł:

Competition hypergraphs of digraphs with certain properties II. Hamiltonicity

Autorzy:

Sonntag, Martin
Teichert, Hanns-Martin

Powiązania:

https://bibliotekanauki.pl/articles/743489.pdf

Data publikacji:

2008

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

hypergraph
competition graph
hamiltonian digraph

Opis:

If D = (V,A) is a digraph, its competition hypergraph (D) has vertex set V and e ⊆ V is an edge of (D) iff |e| ≥ 2 and there is a vertex v ∈ V, such that $e = N_D⁻(v) = {w ∈ V|(w,v) ∈ A}$. We give characterizations of (D) in case of hamiltonian digraphs D and, more general, of digraphs D having a τ-cycle factor. The results are closely related to the corresponding investigations for competition graphs in Fraughnaugh et al. [4] and Guichard [6].

Źródło:

Discussiones Mathematicae Graph Theory; 2008, 28, 1; 23-34
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 24.

Tytuł:

On the Hypercompetition Numbers of Hypergraphs with Maximum Degree at Most Two

Autorzy:

Sano, Yoshio

Powiązania:

https://bibliotekanauki.pl/articles/31339316.pdf

Data publikacji:

2015-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
competition hypergraph
hypercompetition number

Opis:

In this note, we give an easy and short proof for the theorem by Park and Kim stating that the hypercompetition numbers of hypergraphs with maximum degree at most two is at most two.

Źródło:

Discussiones Mathematicae Graph Theory; 2015, 35, 3; 595-598
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 25.

Tytuł:

Some Results on 4-Transitive Digraphs

Autorzy:

García-Vázquez, Patricio Ricardo
Hernández-Cruz, César

Powiązania:

https://bibliotekanauki.pl/articles/31342166.pdf

Data publikacji:

2017-02-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

4-transitive digraph
k -transitive digraph
3-kernel
k -kernel
Laborde-Payan-Xuong Conjecture

Opis:

Let D be a digraph with set of vertices V and set of arcs A. We say that D is k-transitive if for every pair of vertices u, v ∈ V, the existence of a uv-path of length k in D implies that (u, v) ∈ A. A 2-transitive digraph is a transitive digraph in the usual sense. A subset N of V is k-independent if for every pair of vertices u, v ∈ N, we have d(u, v), d(v, u) ≥ k; it is l-absorbent if for every u ∈ V \ N there exists v ∈ N such that d(u, v) ≤ l. A k-kernel of D is a k-independent and (k − 1)-absorbent subset of V. The problem of determining whether a digraph has a k-kernel is known to be NP-complete for every k ≥ 2. In this work, we characterize 4-transitive digraphs having a 3-kernel and also 4-transitive digraphs having a 2-kernel. Using the latter result, a proof of the Laborde-Payan-Xuong conjecture for 4-transitive digraphs is given. This conjecture establishes that for every digraph D, an independent set can be found such that it intersects every longest path in D. Also, Seymour’s Second Neighborhood Conjecture is verified for 4-transitive digraphs and further problems are proposed.

Źródło:

Discussiones Mathematicae Graph Theory; 2017, 37, 1; 117-129
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 26.

Tytuł:

The Laplacian spectrum of some digraphs obtained from the wheel

Autorzy:

Su, Li
Li, Hong-Hai
Zheng, Liu-Rong

Powiązania:

https://bibliotekanauki.pl/articles/743220.pdf

Data publikacji:

2012

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
Laplacian matrix
eigenvalue
wheel

Opis:

The problem of distinguishing, in terms of graph topology, digraphs with real and partially non-real Laplacian spectra is important for applications. Motivated by the question posed in [R. Agaev, P. Chebotarev, Which digraphs with rings structure are essentially cyclic?, Adv. in Appl. Math. 45 (2010), 232-251], in this paper we completely list the Laplacian eigenvalues of some digraphs obtained from the wheel digraph by deleting some arcs.

Źródło:

Discussiones Mathematicae Graph Theory; 2012, 32, 2; 255-261
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 27.

Tytuł:

A proof of mengers theorem by contraction

Autorzy:

Göring, Frank

Powiązania:

https://bibliotekanauki.pl/articles/743549.pdf

Data publikacji:

2002

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

connectivity
disjoint paths
digraph
Menger

Opis:

A short proof of the classical theorem of Menger concerning the number of disjoint AB-paths of a finite graph for two subsets A and B of its vertex set is given. The main idea of the proof is to contract an edge of the graph.

Źródło:

Discussiones Mathematicae Graph Theory; 2002, 22, 1; 111-112
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 28.

Tytuł:

Sharp Upper Bounds on the Signless Laplacian Spectral Radius of Strongly Connected Digraphs

Autorzy:

Xi, Weige
Wang, Ligong

Powiązania:

https://bibliotekanauki.pl/articles/31340590.pdf

Data publikacji:

2016-11-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
signless Laplacian spectral radius

Opis:

Let \( G = (V (G),E(G)) \) be a simple strongly connected digraph and \( q(G) \) be the signless Laplacian spectral radius of \( G \). For any vertex \( v_i \in V (G) \), let \( d+i \) denote the outdegree of \( v_i \), \( m_i^+ \) denote the average 2-outdegree of \( v_i \), and \( N_i^+ \) denote the set of out-neighbors of \( v_i \). In this paper, we prove that: (1) \( q(G) = d_1^+ + d_2^+, (d_1^+ \ne d_2^+ ) \) if and only if \( G \) is a star digraph \( \overleftrightarrow{K}_{1,n-1} \), where \( d_1^+ \), \( d_2^+ \) are the maximum and the second maximum outdegree, respectively (\( \overleftrightarrow{K}_{1,n-1} \) is the digraph on \( n \) vertices obtained from a star graph \( K_{1,n−1} \) by replacing each edge with a pair of oppositely directed arcs). (2) \( q(G) \le \text{max} \bigg\{ \frac{1}{2} \left( d_i^+ + \sqrt{ { d_i^+ }^2 + 8d_i^+ m_i^+ } \right) : v_i \in V(G) \bigg\} \) with equality if and only if \( G \) is a regular digraph. (3) \( q(G) \le \text{max} \bigg\{ \frac{1}{2} \left( d_i^+ + \sqrt{ {d_i^+}^2 + \frac{4}{d_i^+} \sum_{v_j \in N_i^+ } d_j^+ ( d_j^+ + m_j^+ ) } \right) : v_i \in V(G) \bigg\} \). Moreover, the equality holds if and only if \( G \) is a regular digraph or a bipartite semiregular digraph. (4) \( q(G) \le \text{max} \big\{ \frac{1}{2} \left( d_i^+ + 2d_j^+ - 1 + \sqrt{ ( d_i^+ - 2d_j^+ + 1 )^2 + 4d_i^+ } \right) : ( v_j, v_i ) \in E(G) \big\} \). If the equality holds, then \( G \) is a regular digraph or \( G \in \Omega \), where \( \Omega \) is a class of digraphs defined in this paper.

Źródło:

Discussiones Mathematicae Graph Theory; 2016, 36, 4; 977-988
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 29.

Tytuł:

T_r -Span of Directed Wheel Graphs

Autorzy:

Besson, Marc
Tesman, Barry

Powiązania:

https://bibliotekanauki.pl/articles/31342270.pdf

Data publikacji:

2018-11-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

T -coloring
digraph
wheel graph
span

Opis:

In this paper, we consider T-colorings of directed graphs. In particular, we consider as a T-set the set T_r = {0, 1, 2, . . ., r−1, r+1, . . .}. Exact values and bounds of the T_r-span of directed graphs whose underlying graph is a wheel graph are presented.

Źródło:

Discussiones Mathematicae Graph Theory; 2018, 38, 4; 871-888
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 30.

Tytuł:

Orientable $ \mathbb{Z}_N $-Distance Magic Graphs

Autorzy:

Cichacz, Sylwia
Freyberg, Bryan
Froncek, Dalibor

Powiązania:

https://bibliotekanauki.pl/articles/31343411.pdf

Data publikacji:

2019-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

distance magic graph
digraph
flow graph

Opis:

Let $ G = (V, E) $ be a graph of order $n$. A distance magic labeling of $G$ is a bijection $ \mathcal{l}: V \rightarrow {1, 2, . . ., n} $ for which there exists a positive integer $k$ such that $ \Sigma_{ x \in N(v) } \mathcal{l} (x) = k $ for all $ v \in V $, where $ N(v) $ is the open neighborhood of $v$. Tuttes flow conjectures are a major source of inspiration in graph theory. In this paper we ask when we can assign $n$ distinct labels from the set $ {1, 2, . . ., n} $ to the vertices of a graph $G$ of order $n$ such that the sum of the labels on heads minus the sum of the labels on tails is constant modulo $n$ for each vertex of $G$. Therefore we generalize the notion of distance magic labeling for oriented graphs.

Źródło:

Discussiones Mathematicae Graph Theory; 2019, 39, 2; 533-546
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

Artykuł

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Skocz do pozycji: 31.

Tytuł:

Extremal Digraphs Avoiding Distinct Walks of Length 4 with the Same Endpoints

Autorzy:

Lyu, Zhenhua

Powiązania:

https://bibliotekanauki.pl/articles/32304139.pdf

Data publikacji:

2022-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
Turán problems
transitive tournament
walk

Opis:

Let n ≥ 8 be an integer. We characterize the extremal digraphs of order n with the maximum number of arcs avoiding distinct walks of length 4 with the same endpoints.

Źródło:

Discussiones Mathematicae Graph Theory; 2022, 42, 3; 985-1004
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

Artykuł

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Skocz do pozycji: 32.

Tytuł:

Minimal positive realizations of linear continuous-time fractional descriptor systems: Two cases of an input-output digraph structure

Autorzy:

Markowski, K. A.

Powiązania:

https://bibliotekanauki.pl/articles/330387.pdf

Data publikacji:

2018

Wydawca:

Uniwersytet Zielonogórski. Oficyna Wydawnicza

Tematy:

fractional system
positive system
descriptor system
digraph structure
digraph mask
układ ułamkowy
układ dodatni
układ deskryptorowy

Opis:

In the last two decades, fractional calculus has become a subject of great interest in various areas of physics, biology, economics and other sciences. The idea of such a generalization was mentioned by Leibniz and L'Hospital. Fractional calculus has been found to be a very useful tool for modeling linear systems. In this paper, a method for computation of a set of a minimal positive realization of a given transfer function of linear fractional continuous-time descriptor systems has been presented. The proposed method is based on digraph theory. Also, two cases of a possible input-output digraph structure are investigated and discussed. It should be noted that a digraph mask is introduced and used for the first time to solve a minimal positive realization problem. For the presented method, an algorithm was also constructed. The proposed solution allows minimal digraph construction for any one-dimensional fractional positive system. The proposed method is discussed and illustrated in detail with some numerical examples.

Źródło:

International Journal of Applied Mathematics and Computer Science; 2018, 28, 1; 9-24
1641-876X
2083-8492

Pojawia się w:

International Journal of Applied Mathematics and Computer Science

Dostawca treści:

Biblioteka Nauki

/5

Artykuł

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Skocz do pozycji: 33.

Tytuł:

Degree sequences of digraphs with highly irregular property

Autorzy:

Majcher, Zofia
Michael, Jerzy

Powiązania:

https://bibliotekanauki.pl/articles/972042.pdf

Data publikacji:

1998

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
degree sequence
highly irregular property

Opis:

A digraph such that for each its vertex, vertices of the out-neighbourhood have different in-degrees and vertices of the in-neighbourhood have different out-degrees, will be called an HI-digraph. In this paper, we give a characterization of sequences of pairs of out- and in-degrees of HI-digraphs.

Źródło:

Discussiones Mathematicae Graph Theory; 1998, 18, 1; 49-61
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

Artykuł

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Skocz do pozycji: 34.

Tytuł:

Difference labelling of digraphs

Autorzy:

Sonntag, Martin

Powiązania:

https://bibliotekanauki.pl/articles/744591.pdf

Data publikacji:

2004

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

graph labelling
difference digraph
oriented tree

Opis:

A digraph G is a difference digraph iff there exists an S ⊂ N⁺ such that G is isomorphic to the digraph DD(S) = (V,A), where V = S and A = {(i,j):i,j ∈ V ∧ i-j ∈ V}.For some classes of digraphs, e.g. alternating trees, oriented cycles, tournaments etc., it is known, under which conditions these digraphs are difference digraphs (cf. [5]). We generalize the so-called source-join (a construction principle to obtain a new difference digraph from two given ones (cf. [5])) and construct a difference labelling for the source-join of an even number of difference digraphs. As an application we obtain a sufficient condition guaranteeing that certain (non-alternating) trees are difference digraphs.

Źródło:

Discussiones Mathematicae Graph Theory; 2004, 24, 3; 509-527
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 35.

Tytuł:

Power on digraphs

Autorzy:

Peters, H.
Timmer, J.
van den Brink, R.

Powiązania:

https://bibliotekanauki.pl/articles/406504.pdf

Data publikacji:

2016

Wydawca:

Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej

Tematy:

digraph
power index
transfer property
link addition

Opis:

It is assumed that relations between n players are represented by a directed graph or digraph. Such a digraph is called invariant if there is a link (arc) between any two players between whom there is also a directed path. We characterize a class of power indices for invariant digraphs based on four axioms: Null player, Constant sum, Anonymity, and the Transfer property. This class is determined by 2n – 2 parameters. By considering additional conditions about the effect of adding a directed link between two players, we single out three different, one-parameter families of power indices, reflecting several well- -known indices from the literature: the Copeland score, β- and apex type indices.

Źródło:

Operations Research and Decisions; 2016, 26, 2; 107-125
2081-8858
2391-6060

Pojawia się w:

Operations Research and Decisions

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 36.

Tytuł:

On (k,l)-kernel perfectness of special classes of digraphs

Autorzy:

Kucharska, Magdalena

Powiązania:

https://bibliotekanauki.pl/articles/744319.pdf

Data publikacji:

2005

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

kernel
(k,l)-kernel
kernel-perfect digraph

Opis:

In the first part of this paper we give necessary and sufficient conditions for some special classes of digraphs to have a (k,l)-kernel. One of them is the duplication of a set of vertices in a digraph. This duplication come into being as the generalization of the duplication of a vertex in a graph (see [4]). Another one is the D-join of a digraph D and a sequence α of nonempty pairwise disjoint digraphs. In the second part we prove theorems, which give necessary and sufficient conditions for special digraphs presented in the first part to be (k,l)-kernel-perfect digraphs. The concept of a (k,l)-kernel-perfect digraph is the generalization of the well-know idea of a kernel perfect digraph, which was considered in [1] and [6].

Źródło:

Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 103-119
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 37.

Tytuł:

On Decomposing the Complete Symmetric Digraph into Orientations of K₄ − e

Autorzy:

Bunge, Ryan C.
Darrow, Brian D.
Dubczuk, Toni M.
El-Zanati, Saad I.
Hao, Hanson H.
Keller, Gregory L.
Newkirk, Genevieve A.
Roberts, Dan P.

Powiązania:

https://bibliotekanauki.pl/articles/31343235.pdf

Data publikacji:

2019-11-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph decompositions
orientations of K 4 − e

Opis:

Let $D$ be any of the 10 digraphs obtained by orienting the edges of $ K_4 − e $. We establish necessary and sufficient conditions for the existence of a $ (K_n^*, D)$-design for 8 of these digraphs. Partial results as well as some nonexistence results are established for the remaining 2 digraphs.

Źródło:

Discussiones Mathematicae Graph Theory; 2019, 39, 4; 815-828
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 38.

Tytuł:

Research on SDG fault diagnosis of ocean shipping boiler system based on fuzzy granular computing under data fusion

Autorzy:

Zhu, Y.
Geng, L.

Powiązania:

https://bibliotekanauki.pl/articles/258772.pdf

Data publikacji:

2018

Wydawca:

Politechnika Gdańska. Wydział Inżynierii Mechanicznej i Okrętownictwa

Tematy:

granular computing
symbolic digraph
fault diagnosis
fuzzy theory

Opis:

The research work in this paper belongs to the application of granular computing, graph theory and its application in fault detection and diagnosis. It is a cross cutting and frontier research field in computer science, information science and graph theory. The results of this paper are of great significance to the application of the fault detection and diagnosis of the ocean boilers system. This research combines granular computing theory and signed directed graph, and proposes a new method of fault diagnosis, and applies it to the fault diagnosis of ocean ship boiler system.

Źródło:

Polish Maritime Research; 2018, S 2; 92-97
1233-2585

Pojawia się w:

Polish Maritime Research

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 39.

Tytuł:

Decompositions of a complete multidigraph into almost arbitrary paths

Autorzy:

Meszka, Mariusz
Skupień, Zdzisław

Powiązania:

https://bibliotekanauki.pl/articles/743246.pdf

Data publikacji:

2012

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

complete digraph
multidigraph
tour girth
arbitrary path decomposition

Opis:

For n ≥ 4, the complete n-vertex multidigraph with arc multiplicity λ is proved to have a decomposition into directed paths of arbitrarily prescribed lengths ≤ n - 1 and different from n - 2, unless n = 5, λ = 1, and all lengths are to be n - 1 = 4. For λ = 1, a more general decomposition exists; namely, up to five paths of length n - 2 can also be prescribed.

Źródło:

Discussiones Mathematicae Graph Theory; 2012, 32, 2; 357-372
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 40.

Tytuł:

(k,l)-kernels, (k,l)-semikernels, k-Grundy functions and duality for state splittings

Autorzy:

Galeana-Sánchez, Hortensia
Gómez, Ricardo

Powiązania:

https://bibliotekanauki.pl/articles/743799.pdf

Data publikacji:

2007

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

state splitting
line digraph
kernel
Grundy function
duality

Opis:

Line digraphs can be obtained by sequences of state splittings, a particular kind of operation widely used in symbolic dynamics [12]. Properties of line digraphs inherited from the source have been studied, for instance in [7] Harminc showed that the cardinalities of the sets of kernels and solutions (kernel's dual definition) of a digraph and its line digraph coincide. We extend this for (k,l)-kernels in the context of state splittings and also look at (k,l)-semikernels, k-Grundy functions and their duals.

Źródło:

Discussiones Mathematicae Graph Theory; 2007, 27, 2; 359-371
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 41.

Tytuł:

The Double Roman Domatic Number of a Digraph

Autorzy:

Volkmann, Lutz

Powiązania:

https://bibliotekanauki.pl/articles/31348166.pdf

Data publikacji:

2020-11-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
double Roman domination
double Roman domatic number

Opis:

A double Roman dominating function on a digraph $D$ with vertex set $V(D)$ is defined in [G. Hao, X. Chen and L. Volkmann, Double Roman domination in digraphs, Bull. Malays. Math. Sci. Soc. (2017).] as a function $f : V (D) → {0, 1, 2, 3}$ having the property that if $f(v) = 0$, then the vertex $v$ must have at least two in-neighbors assigned 2 under $f$ or one in-neighbor w with $f(w) = 3$, and $if f(v) = 1$, then the vertex v must have at least one in-neighbor $u$ with $f(u) ≥ 2$. A set ${f_1, f_2, . . ., f_d}$ of distinct double Roman dominating functions on $D$ with the property that $∑_{i=1}^df_i(v)≤3$ for each $v ∈ V (D)$ is called a double Roman dominating family (of functions) on $D$. The maximum number of functions in a double Roman dominating family on $D$ is the double Roman domatic number of $D$, denoted by $d_{dR}(D)$. We initiate the study of the double Roman domatic number, and we present different sharp bounds on $d_{dR}(D)$. In addition, we determine the double Roman domatic number of some classes of digraphs.

Źródło:

Discussiones Mathematicae Graph Theory; 2020, 40, 4; 995-1004
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 42.

Tytuł:

On the existence of (k,l)-kernels in infinite digraphs: A survey

Autorzy:

Galeana-Sánchez, H.
Hernández-Cruz, C.

Powiązania:

https://bibliotekanauki.pl/articles/30148241.pdf

Data publikacji:

2014-08-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

kernel
k-kernel
infinite digraph
(k, l)-kernel

Opis:

Let D be a digraph, V (D) and A(D) will denote the sets of vertices and arcs of D, respectively. A (k, l)-kernel N of D is a k-independent (if u, v ∈ N, u 6= v, then d(u, v), d(v, u) ≥ k) and l-absorbent (if u ∈ V (D) − N then there exists v ∈ N such that d(u, v) ≤ l) set of vertices. A k-kernel is a (k, k −1)-kernel. This work is a survey of results proving sufficient conditions for the existence of (k, l)-kernels in infinite digraphs. Despite all the previous work in this direction was done for (2, 1)-kernels, we present many original results concerning (k, l)-kernels for distinct values of k and l. The original results are sufficient conditions for the existence of (k, l)- kernels in diverse families of infinite digraphs. Among the families that we study are: transitive digraphs, quasi-transitive digraphs, right/left pretransitive digraphs, cyclically k-partite digraphs, κ-strong digraphs, k-transitive digraphs, k-quasi-transitive digraphs.

Źródło:

Discussiones Mathematicae Graph Theory; 2014, 34, 3; 431-466
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 43.

Tytuł:

γ-Cycles And Transitivity By Monochromatic Paths In Arc-Coloured Digraphs

Autorzy:

Casas-Bautista, Enrique
Galeana-Sánchez, Hortensia
Rojas-Monroy, Rocío

Powiązania:

https://bibliotekanauki.pl/articles/30146505.pdf

Data publikacji:

2013-07-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
kernel
kernel by monochromatic paths
γ-cycle

Opis:

We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. If D is an m-coloured digraph and a ∈ A(D), colour(a) will denote the colour has been used on a. A path (or a cycle) is called monochromatic if all of its arcs are coloured alike. A γ-cycle in D is a sequence of vertices, say γ = (u₀, u₁, . . ., u_n), such that u_i ≠ u_j if i ≠ j and for every i ∈ {0, 1, . . ., n} there is a u_iu_i+1-monochromatic path in D and there is no u_i+1u_i-monochromatic path in D (the indices of the vertices will be taken mod n+1). A set N ⊆ V (D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions: (i) for every pair of different vertices u, v ∈ N there is no monochromatic path between them and; (ii) for every vertex x ∈ V (D) \ N there is a vertex y ∈ N such that there is an xy-monochromatic path. Let D be a finite m-coloured digraph. Suppose that {C₁,C₂} is a partition of C, the set of colours of D, and D_i will be the spanning subdigraph of D such that A(D_i) = {a ∈ A(D) | colour(a) ∈ C_i}. In this paper, we give some sufficient conditions for the existence of a kernel by monochromatic paths in a digraph with the structure mentioned above. In particular we obtain an extension of the original result by B. Sands, N. Sauer and R. Woodrow that asserts: Every 2-coloured digraph has a kernel by monochromatic paths. Also, we extend other results obtained before where it is proved that under some conditions an m-coloured digraph has no γ-cycles.

Źródło:

Discussiones Mathematicae Graph Theory; 2013, 33, 3; 493-507
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 44.

Tytuł:

Frucht’s Theorem for the Digraph Factorial

Autorzy:

Hammack, Richard H.

Powiązania:

https://bibliotekanauki.pl/articles/30146632.pdf

Data publikacji:

2013-05-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

Frucht’s theorem
digraphs
graph automorphisms
digraph factorial

Opis:

To every graph (or digraph) A, there is an associated automorphism group Aut(A). Frucht’s theorem asserts the converse association; that for any finite group G there is a graph (or digraph) A for which Aut(A) ≅ G. A new operation on digraphs was introduced recently as an aid in solving certain questions regarding cancellation over the direct product of digraphs. Given a digraph A, its factorial A! is certain digraph whose vertex set is the permutations of V (A). The arc set E(A!) forms a group, and the loops form a subgroup that is isomorphic to Aut(A). (So E(A!) can be regarded as an extension of Aut(A).) This note proves an analogue of Frucht’s theorem in which Aut(A) is replaced by the group E(A!). Given any finite group G, we show that there is a graph A for which E(A!) ≅ G.

Źródło:

Discussiones Mathematicae Graph Theory; 2013, 33, 2; 329-336
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 45.

Tytuł:

Isomorphisms and traversability of directed path graphs

Autorzy:

Broersma, Hajo
Li, Xueliang

Powiązania:

https://bibliotekanauki.pl/articles/743350.pdf

Data publikacji:

2002

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

directed path graph
line digraph
isomorphism
travers-ability

Opis:

The concept of a line digraph is generalized to that of a directed path graph. The directed path graph Pₖ(D) of a digraph D is obtained by representing the directed paths on k vertices of D by vertices. Two vertices are joined by an arc whenever the corresponding directed paths in D form a directed path on k+1 vertices or form a directed cycle on k vertices in D. In this introductory paper several properties of P₃(D) are studied, in particular with respect to isomorphism and traversability. In our main results, we characterize all digraphs D with P₃(D) ≅ D, we show that P₃(D₁) ≅ P₃(D₂) "almost always" implies D₁ ≅ D₂, and we characterize all digraphs with Eulerian or Hamiltonian P₃-graphs.

Źródło:

Discussiones Mathematicae Graph Theory; 2002, 22, 2; 215-228
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 46.

Tytuł:

In-degree sequence in a general model of a random digraph

Autorzy:

Palka, Zbigniew
Sperling, Monika

Powiązania:

https://bibliotekanauki.pl/articles/743920.pdf

Data publikacji:

2006

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

degree sequence
general model of a random digraph

Opis:

A general model of a random digraph D(n,P) is considered. Based on a precise estimate of the asymptotic behaviour of the distribution function of the binomial law, a problem of the distribution of extreme in-degrees of D(n,P) is discussed.

Źródło:

Discussiones Mathematicae Graph Theory; 2006, 26, 2; 193-207
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 47.

Tytuł:

On uniquely partitionable relational structures and object systems

Autorzy:

Bucko, Jozef
Mihók, Peter

Powiązania:

https://bibliotekanauki.pl/articles/743971.pdf

Data publikacji:

2006

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

graph
digraph
hypergraph
vertex colouring
uniquely partitionable system

Opis:

We introduce object systems as a common generalization of graphs, hypergraphs, digraphs and relational structures. Let C be a concrete category, a simple object system over C is an ordered pair S = (V,E), where E = {A₁,A₂,...,Aₘ} is a finite set of the objects of C, such that the ground-set $V(A_i)$ of each object $A_i ∈ E$ is a finite set with at least two elements and $V ⊇ ⋃_{i=1}^m V(A_i)$. To generalize the results on graph colourings to simple object systems we define, analogously as for graphs, that an additive induced-hereditary property of simple object systems over a category C is any class of systems closed under isomorphism, induced-subsystems and disjoint union of systems, respectively. We present a survey of recent results and conditions for object systems to be uniquely partitionable into subsystems of given properties.

Źródło:

Discussiones Mathematicae Graph Theory; 2006, 26, 2; 281-289
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

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Skocz do pozycji: 48.

Tytuł:

On independent sets and non-augmentable paths in directed graphs

Autorzy:

Galeana-Sánchez, H.

Powiązania:

https://bibliotekanauki.pl/articles/744219.pdf

Data publikacji:

1998

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
independent set
directed path
non-augmentable path

Opis:

We investigate sufficient conditions, and in case that D be an asymmetrical digraph a necessary and sufficient condition for a digraph to have the following property: "In any induced subdigraph H of D, every maximal independent set meets every non-augmentable path". Also we obtain a necessary and sufficient condition for any orientation of a graph G results a digraph with the above property. The property studied in this paper is an instance of the property of a conjecture of J.M. Laborde, Ch. Payan and N.H. Huang: "Every digraph contains an independent set which meets every longest directed path" (1982).

Źródło:

Discussiones Mathematicae Graph Theory; 1998, 18, 2; 171-181
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 49.

Tytuł:

$ \gamma $-Cycles In Arc-Colored Digraphs

Autorzy:

Galeana-Sánchez, Hortensia
Gaytán-Gómez, Guadalupe
Rojas-Monroy, Rocío

Powiązania:

https://bibliotekanauki.pl/articles/31341163.pdf

Data publikacji:

2016-02-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph
kernel
kernel by monochromatic paths
γ-cycle

Opis:

We call a digraph $D$ an $m$-colored digraph if the arcs of $D$ are colored with $m$ colors. A directed path (or a directed cycle) is called monochromatic if all of its arcs are colored alike. A subdigraph $H$ in $D$ is called rainbow if all of its arcs have different colors. A set $ N \subseteq V (D) $ is said to be a kernel by monochromatic paths of $D$ if it satisfies the two following conditions: (i) for every pair of different vertices $ u, v \in N $ there is no monochromatic path in $D$ between them, and (ii) for every vertex $ x \in V (D) − N $ there is a vertex $ y \in N $ such that there is an $xy$-monochromatic path in $D$. A $\gamma$-cycle in $D$ is a sequence of different vertices $ \gamma = (u_0, u_1, . . ., u_n, u_0)$ such that for every $ i \in {0, 1, . . ., n}$: (i) there is a $u_i u_{i+1}$-monochromatic path, and (ii) there is no $u_{i+1}u_i$-monochromatic path. The addition over the indices of the vertices of $ \gamma $ is taken modulo $(n + 1)$. If $D$ is an $m$-colored digraph, then the closure of $D$, denoted by $ \mathfrak{C}(D)$, is the $m$-colored multidigraph defined as follows: $ V (\mathfrak{C} (D)) = V (D) $, $ A( \mathfrak{C} (D)) = A(D) \cup \{ (u, v) $ with color $i$ | there exists a $uv$-monochromatic path colored $i$ contained in $D \} $. In this work, we prove the following result. Let $D$ be a finite m-colored digraph which satisfies that there is a partition $ C = C_1 \cup C_2 $ of the set of colors of $D$ such that: (1) $ D[ \hat{C}_i ] $ (the subdigraph spanned by the arcs with colors in $ C_i) $ contains no $ \gamma $-cycles for $ i \in {1, 2} $; (2) If $ \mathfrak{C}(D) $ contains a rainbow $ C_3 = (x_0, z, w, x_0) $ involving colors of $ C_1 $ and $ C_2 $, then $ (x_0, w) \in A(\mathfrak{C} (D)) $ or $ (z, x_0) \in A( \mathfrak{C} (D)) $; (3) If $ \mathfrak{C}(D) $ contains a rainbow $ P_3 = (u, z, w, x_0) $ involving colors of $ C_1 $ and $ C_2 $, then at least one of the following pairs of vertices is an arc in $ \mathfrak{C} (D) $: $ (u, w) $, $ (w, u) $, $ (x_0, u) $, $ (u, x_0) $, $ (x_0, w) $, $ (z, u) $, $ (z, x_0) $. Then $D$ has a kernel by monochromatic paths. This theorem can be applied to all those digraphs that contain no $ \gamma $-cycles. Generalizations of many previous results are obtained as a direct consequence of this theorem.

Źródło:

Discussiones Mathematicae Graph Theory; 2016, 36, 1; 103-116
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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Skocz do pozycji: 50.

Tytuł:

Oriented Incidence Colourings of Digraphs

Autorzy:

Duffy, Christopher
MacGillivray, Gary
Ochem, Pascal
Raspaud, André

Powiązania:

https://bibliotekanauki.pl/articles/31343581.pdf

Data publikacji:

2019-02-01

Wydawca:

Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii

Tematy:

digraph homomorpism
graph colouring
incidence colouring
computational complexity

Opis:

Brualdi and Quinn Massey [6] defined incidence colouring while studying the strong edge chromatic index of bipartite graphs. Here we introduce a similar concept for digraphs and define the oriented incidence chromatic number. Using digraph homomorphisms, we show that the oriented incidence chromatic number of a digraph is closely related to the chromatic number of the underlying simple graph. This motivates our study of the oriented incidence chromatic number of symmetric complete digraphs. We give upper and lower bounds for the oriented incidence chromatic number of these graphs, as well as digraphs arising from common graph constructions and decompositions. Additionally we construct, for all k > 2, a target digraph H_k for which oriented incidence k colouring is equivalent to homomorphism to H_k.

Źródło:

Discussiones Mathematicae Graph Theory; 2019, 39, 1; 191-210
2083-5892

Pojawia się w:

Discussiones Mathematicae Graph Theory

Dostawca treści:

Biblioteka Nauki

/5

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