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Wyświetlanie 1-15 z 65
Tytuł:
Graphs with convex domination number close to their order
Autorzy:
Cyman, Joanna
Lemańska, Magdalena
Raczek, Joanna
Powiązania:
https://bibliotekanauki.pl/articles/743979.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
convex domination
Cartesian product
Opis:
For a connected graph G = (V,E), a set D ⊆ V(G) is a dominating set of G if every vertex in V(G)-D has at least one neighbour in D. The distance $d_G(u,v)$ between two vertices u and v is the length of a shortest (u-v) path in G. An (u-v) path of length $d_G(u,v)$ is called an (u-v)-geodesic. A set X ⊆ V(G) is convex in G if vertices from all (a-b)-geodesics belong to X for any two vertices a,b ∈ X. A set X is a convex dominating set if it is convex and dominating. The convex domination number $γ_{con}(G)$ of a graph G is the minimum cardinality of a convex dominating set in G. Graphs with the convex domination number close to their order are studied. The convex domination number of a Cartesian product of graphs is also considered.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 2; 307-316
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Separation of Cartesian Products of Graphs Into Several Connected Components by the Removal of Vertices
Autorzy:
Erker, Tjaša Paj
Špacapan, Simon
Powiązania:
https://bibliotekanauki.pl/articles/32304144.pdf
Data publikacji:
2022-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
k -connectivity
Cartesian product
Opis:
A set S ⊆ V (G) is a vertex k-cut in a graph G = (V (G), E(G)) if G − S has at least k connected components. The k-connectivity of G, denoted as κk(G), is the minimum cardinality of a vertex k-cut in G. We give several constructions of a set S such that (G□H) − S has at least three connected components. Then we prove that for any 2-connected graphs G and H, of order at least six, one of the defined sets S is a minimum vertex 3-cut in G□H. This yields a formula for κ3(G□H).
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 3; 905-920
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Vizings conjecture
Autorzy:
Bresar, Bostjan
Powiązania:
https://bibliotekanauki.pl/articles/743820.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
Cartesian product
domination number
Opis:
A dominating set D for a graph G is a subset of V(G) such that any vertex in V(G)-D has a neighbor in D, and a domination number γ(G) is the size of a minimum dominating set for G. For the Cartesian product G ⃞ H Vizing's conjecture [10] states that γ(G ⃞ H) ≥ γ(G)γ(H) for every pair of graphs G,H. In this paper we introduce a new concept which extends the ordinary domination of graphs, and prove that the conjecture holds when γ(G) = γ(H) = 3.
Źródło:
Discussiones Mathematicae Graph Theory; 2001, 21, 1; 5-11
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On dominating the Cartesian product of a graph and K₂
Autorzy:
Hartnell, Bert
Rall, Douglas
Powiązania:
https://bibliotekanauki.pl/articles/744535.pdf
Data publikacji:
2004
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
domination
2-packing, Cartesian product
Opis:
In this paper we consider the Cartesian product of an arbitrary graph and a complete graph of order two. Although an upper and lower bound for the domination number of this product follow easily from known results, we are interested in the graphs that actually attain these bounds. In each case, we provide an infinite class of graphs to show that the bound is sharp. The graphs that achieve the lower bound are of particular interest given the special nature of their dominating sets and are investigated further.
Źródło:
Discussiones Mathematicae Graph Theory; 2004, 24, 3; 389-402
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Thickness of Amalgamations and Cartesian Product of Graphs
Autorzy:
Yang, Yan
Chen, Yichao
Powiązania:
https://bibliotekanauki.pl/articles/31341728.pdf
Data publikacji:
2017-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
thickness
amalgamation
Cartesian product
genus
Opis:
The thickness of a graph is the minimum number of planar spanning subgraphs into which the graph can be decomposed. It is a measurement of the closeness to the planarity of a graph, and it also has important applications to VLSI design, but it has been known for only few graphs. We obtain the thickness of vertex-amalgamation and bar-amalgamation of graphs, the lower and upper bounds for the thickness of edge-amalgamation and 2-vertex-amalgamation of graphs, respectively. We also study the thickness of Cartesian product of graphs, and by using operations on graphs, we derive the thickness of the Cartesian product Kn □ Pm for most values of m and n.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 3; 561-572
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Crossing Number of Cartesian Product of 5-Wheel with any Tree
Autorzy:
Wang, Yuxi
Huang, Yuanqiu
Powiązania:
https://bibliotekanauki.pl/articles/32083823.pdf
Data publikacji:
2021-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
drawing
crossing number
join product
Cartesian product
Opis:
In this paper, we establish the crossing number of join product of 5-wheel with n isolated vertices. In addition, the exact values for the crossing numbers of Cartesian products of the wheels of order at most five with any tree T are given.
Źródło:
Discussiones Mathematicae Graph Theory; 2021, 41, 1; 183-197
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The domination number of $K_n^3$
Autorzy:
Georges, John
Lin, Jianwei
Mauro, David
Powiązania:
https://bibliotekanauki.pl/articles/30148694.pdf
Data publikacji:
2014-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
Cartesian product
dominating set
domination number
Opis:
Let $K_n^3$ denote the Cartesian product $K_n□K_n□K_n$, where $K_n$ is the complete graph on $n$ vertices. We show that the domination number of $K_n^3$ is $⌈\frac{n^2}{2}⌉$.
Źródło:
Discussiones Mathematicae Graph Theory; 2014, 34, 3; 629-632
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The metric dimension of circulant graphs and their Cartesian products
Autorzy:
Chau, K.
Gosselin, S.
Powiązania:
https://bibliotekanauki.pl/articles/255804.pdf
Data publikacji:
2017
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
metric dimension
circulant graph
Cartesian product
Opis:
Let G = (V, E) be a connected graph (or hypergraph) and let d(x,y) denote the distance between vertices x,y ∈V(G). A subset W ⊆V(G) is called a resolving set for G if for every pair ol distinct vertices x, y ∈ (G), there is w ∈W such that d(x,w) ≠d(y,w). The minimum cardinality of a resolving set for G is called the metric dimension of G, denoted by β (G). The circulant graph Cn(l, 2,... , t) has vertex set {v0, v1 …, vn-1} and edges [formula] where 0 ≤ i ≤ n — 1 and 1 ≤j ≤ t and the indices are taken modulo [formula]. In this paper we determine the exact metric dimension olthe circulant graphs Cn(l, 2,... , t). extending previous results due to Borchert and Gosselin (2013), Grigorious et al. (2014), and Vetrik (2016). In particular, we show that [formula] for large enough n, which implies that the metric dimension ol these circulants is completely determined by the congruence class ol n modulo 2t. We determine the exact value of β Cn (l, 2,.. . , i)) for n ≡ 2 mod 2t and n =≡ (t + 1) mod 2t and we give better bounds on the metric dimension ol these circulants for n ≡ 0 mod 2t and n ≡ 1 mod 2t. In addition, we bound the metric dimension ol Cartesian products ol circulant graphs.
Źródło:
Opuscula Mathematica; 2017, 37, 4; 509-534
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Weak k-reconstruction of Cartesian products
Autorzy:
Imrich, Wilfried
Zmazek, Blaz
Zerovnik, Janez
Powiązania:
https://bibliotekanauki.pl/articles/743162.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
reconstruction problem
Cartesian product
composite graphs
Opis:
By Ulam's conjecture every finite graph G can be reconstructed from its deck of vertex deleted subgraphs. The conjecture is still open, but many special cases have been settled. In particular, one can reconstruct Cartesian products. We consider the case of k-vertex deleted subgraphs of Cartesian products, and prove that one can decide whether a graph H is a k-vertex deleted subgraph of a Cartesian product G with at least k+1 prime factors on at least k+1 vertices each, and that H uniquely determines G. This extends previous work of the authors and Sims. The paper also contains a counterexample to a conjecture of MacAvaney.
Źródło:
Discussiones Mathematicae Graph Theory; 2003, 23, 2; 273-285
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Defining sets in (proper) vertex colorings of the Cartesian product of a cycle with a complete graph
Autorzy:
Mojdeh, D.
Powiązania:
https://bibliotekanauki.pl/articles/743869.pdf
Data publikacji:
2006
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph coloring
defining set
cartesian product
Opis:
In a given graph G = (V,E), a set of vertices S with an assignment of colors to them is said to be a defining set of the vertex coloring of G, if there exists a unique extension of the colors of S to a c ≥ χ(G) coloring of the vertices of G. A defining set with minimum cardinality is called a minimum defining set and its cardinality is the defining number, denoted by d(G,c).
The d(G = Cₘ × Kₙ, χ(G)) has been studied. In this note we show that the exact value of defining number d(G = Cₘ × Kₙ, c) with c > χ(G), where n ≥ 2 and m ≥ 3, unless the defining number $d(K₃×C_{2r},4)$, which is given an upper and lower bounds for this defining number. Also some bounds of defining number are introduced.
Źródło:
Discussiones Mathematicae Graph Theory; 2006, 26, 1; 59-72
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the Crossing Numbers of Cartesian Products of Wheels and Trees
Autorzy:
Klešč, Marián
Petrillová, Jana
Valo, Matúš
Powiązania:
https://bibliotekanauki.pl/articles/31341838.pdf
Data publikacji:
2017-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
drawing
crossing number
join product
Cartesian product
Opis:
Bokal developed an innovative method for finding the crossing numbers of Cartesian product of two arbitrarily large graphs. In this article, the crossing number of the join product of stars and cycles are given. Afterwards, using Bokal’s zip product operation, the crossing numbers of the Cartesian products of the wheel Wn and all trees T with maximum degree at most five are established.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 2; 399-413
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The crossing numbers of certain Cartesian products
Autorzy:
Klešč, Marián
Powiązania:
https://bibliotekanauki.pl/articles/971930.pdf
Data publikacji:
1995
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
drawing
crossing number
path
Cartesian product
Opis:
In this article we determine the crossing numbers of the Cartesian products of given three graphs on five vertices with paths.
Źródło:
Discussiones Mathematicae Graph Theory; 1995, 15, 1; 5-10
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The achromatic number of $K6 \square K7$ is 18
Autorzy:
Horňák, Mirko
Powiązania:
https://bibliotekanauki.pl/articles/2050912.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
complete vertex colouring
achromatic number
Cartesian product
Opis:
A vertex colouring $ƒ: V(G) \rightarrow C$ of a graph $G$ is complete if for any two distinct colours $c_{1},c_{2} \in C$ there is an edge $\{v_{1} ,v_{2}\} \in E(G)$ such that $ƒ(v_{i}) = c_{i}, i = 1, 2$. The achromatic number of G is the maximum number achr(G) of colours in a proper complete vertex colouring of G. In the paper it is proved that achr$(K_{6} \square K_{7})$ = 18. This result finalises the determination of achr$(K_{6} \square K_{q})$.
Źródło:
Opuscula Mathematica; 2021, 41, 2; 163-185
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the crossing numbers of G □ Cₙ for graphs G on six vertices
Autorzy:
Draženská, Emília
Klešč, Marián
Powiązania:
https://bibliotekanauki.pl/articles/743871.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
cycle
drawing
crossing number
Cartesian product
Opis:
The crossing numbers of Cartesian products of paths, cycles or stars with all graphs of order at most four are known. The crossing numbers of G☐Cₙ for some graphs G on five and six vertices and the cycle Cₙ are also given. In this paper, we extend these results by determining crossing numbers of Cartesian products G☐Cₙ for some connected graphs G of order six with six and seven edges. In addition, we collect known results concerning crossing numbers of G☐Cₙ for graphs G on six vertices.
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 2; 239-252
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Path-Pairability in the Cartesian Product of Graphs
Autorzy:
Mészáros, Gábor
Powiązania:
https://bibliotekanauki.pl/articles/31340793.pdf
Data publikacji:
2016-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
path-pairable graphs
Cartesian product of graphs
Opis:
We study the inheritance of path-pairability in the Cartesian product of graphs and prove additive and multiplicative inheritance patterns of path-pairability, depending on the number of vertices in the Cartesian product. We present path-pairable graph families that improve the known upper bound on the minimal maximum degree of a path-pairable graph. Further results and open questions about path-pairability are also presented.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 3; 743-758
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 65

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