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Wyświetlanie 1-15 z 37
Tytuł:
One-Three Join: A Graph Operation and Its Consequences
Autorzy:
Shalu, M.A.
Devi Yamini, S.
Powiązania:
https://bibliotekanauki.pl/articles/31341697.pdf
Data publikacji:
2017-08-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
one-three join
bipartite-join
homogeneous set
odd hole-free graphs
Opis:
In this paper, we introduce a graph operation, namely one-three join. We show that the graph G admits a one-three join if and only if either G is one of the basic graphs (bipartite, complement of bipartite, split graph) or G admits a constrained homogeneous set or a bipartite-join or a join. Next, we define ℳH as the class of all graphs generated from the induced subgraphs of an odd hole-free graph H that contains an odd anti-hole as an induced subgraph by using one-three join and co-join recursively and show that the maximum independent set problem, the maximum clique problem, the minimum coloring problem, and the minimum clique cover problem can be solved efficiently for ℳH.
Źródło:
Discussiones Mathematicae Graph Theory; 2017, 37, 3; 633-647
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
M2-Edge Colorings Of Cacti And Graph Joins
Autorzy:
Czap, Július
Šugerek, Peter
Ivančo, Jaroslav
Powiązania:
https://bibliotekanauki.pl/articles/31341176.pdf
Data publikacji:
2016-02-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
cactus
edge coloring
graph join
Opis:
An edge coloring φ of a graph G is called an M2-edge coloring if |φ(v)| ≤ 2 for every vertex v of G, where φ(v) is the set of colors of edges incident with v. Let K2(G) denote the maximum number of colors used in an M2-edge coloring of G. In this paper we determine K2(G) for trees, cacti, complete multipartite graphs and graph joins.
Źródło:
Discussiones Mathematicae Graph Theory; 2016, 36, 1; 59-69
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The Crossing Numbers of Join of Some Graphs with n Isolated Vertices
Autorzy:
Ding, Zongpeng
Huang, Yuanqiu
Powiązania:
https://bibliotekanauki.pl/articles/31342268.pdf
Data publikacji:
2018-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
disconnected graph
crossing number
join product
Opis:
There are only few results concerning crossing numbers of join of some graphs. In this paper, for some graphs on five vertices, we give the crossing numbers of its join with n isolated vertices.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 4; 899-909
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 crossing numbers of join products of paths with graphs of order four
Autorzy:
Klešč, Marián
Schrötter, Stefan
Powiązania:
https://bibliotekanauki.pl/articles/743896.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
drawing
path
crossing number
join product
Opis:
Kulli and Muddebihal [V.R. Kulli, M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87-97] gave the characterization of all pairs of graphs which join product is planar graph. The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. There are only few results concerning crossing numbers of graphs obtained as join product of two graphs. In the paper, the exact values of crossing numbers for join of paths with all graphs of order four, as well as for join of all graphs of order four with n isolated vertices are given.
Źródło:
Discussiones Mathematicae Graph Theory; 2011, 31, 2; 321-331
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Equivariant maps of joins of finite G-sets and an application to critical point theory
Autorzy:
Rozpłoch-Nowakowska, Danuta
Powiązania:
https://bibliotekanauki.pl/articles/1312198.pdf
Data publikacji:
1992
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
join
group actions
Borsuk's Antipodal Theorem
critical points
Opis:
A lower estimate is proved for the number of critical orbits and critical values of a G-invariant C¹ function $f:S^n → ℝ$, where G is a finite nontrivial group acting freely and orthogonally on $ℝ^{n+1} \ {0}$. Neither Morse theory nor the minimax method is applied. The proofs are based on a general version of Borsuk's Antipodal Theorem for equivariant maps of joins of G-sets.
Źródło:
Annales Polonici Mathematici; 1991-1992, 56, 2; 195-211
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the crossing numbers of join products of five graphs of order six with the discrete graph
Autorzy:
Stas, Michal
Powiązania:
https://bibliotekanauki.pl/articles/952808.pdf
Data publikacji:
2020
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
graph
drawing
crossing number
join product
cyclic permutation
Opis:
The main purpose of this article is broaden known results concerning crossing numbers for join of graphs of order six. We give the crossing number of the join product G* + Dn, where the disconnected graph G* of order six consists of one isolated vertex and of one edge joining two nonadjacent vertices of the 5-cycle. In our proof, the idea of cyclic permutations and their combinatorial properties will be used. Finally, by adding new edges to the graph G*, the crossing numbers of Gi + Dn for four other graphs Gi of order six will be also established
Źródło:
Opuscula Mathematica; 2020, 40, 3; 383-397
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The crossing numbers of join products of paths with three graphs of order five
Autorzy:
Staš, Michal
Švecová, Mária
Powiązania:
https://bibliotekanauki.pl/articles/2216156.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
graph
crossing number
join product
cyclic permutation
path
Opis:
The main aim of this paper is to give the crossing number of the join product $G^∗ + P_n$ for the disconnected graph $G^$∗ of order five consisting of the complete graph $K_4$ and one isolated vertex, where $P_n$ is the path on n vertices. The proofs are done with the help of a lot of well-known exact values for the crossing numbers of the join products of subgraphs of the graph $G^∗$ with the paths. Finally, by adding new edges to the graph $G^∗$, we are able to obtain the crossing numbers of the join products of two other graphs with the path $P_n$.
Źródło:
Opuscula Mathematica; 2022, 42, 4; 635-651
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Cyclic Permutations in Determining Crossing Numbers
Autorzy:
Klešč, Marián
Staš, Michal
Powiązania:
https://bibliotekanauki.pl/articles/32222545.pdf
Data publikacji:
2022-11-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
graph
drawing
crossing number
join product
cyclic permutation
Opis:
The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. Recently, the crossing numbers of join products of two graphs have been studied. In the paper, we extend know results concerning crossing numbers of join products of small graphs with discrete graphs. The crossing number of the join product G*+ Dn for the disconnected graph G* consisting of five vertices and of three edges incident with the same vertex is given. Up to now, the crossing numbers of G + Dn were done only for connected graphs G. In the paper also the crossing numbers of G*+ Pn and G* + Cn are given. The paper concludes by giving the crossing numbers of the graphs H + Dn, H + Pn, and H + Cn for four different graphs H with |E(H)| ≤ |V (H)|. The methods used in the paper are new. They are based on combinatorial properties of cyclic permutations.
Źródło:
Discussiones Mathematicae Graph Theory; 2022, 42, 4; 1163-1183
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 Number of Join of the Generalized Petersen Graph P (3, 1) with Path and Cycle
Autorzy:
Ouyang, Zhang Dong
Wang, Jing
Huang, Yuan Qiu
Powiązania:
https://bibliotekanauki.pl/articles/31342419.pdf
Data publikacji:
2018-05-01
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
crossing number
drawing
join product
generalized Petersen graph
Opis:
There are only few results concerning the crossing numbers of join of some graphs. In this paper, the crossing numbers of join products for the generalized Petersen graph P(3, 1) with n isolated vertices as well as with the path Pn on n vertices and with the cycle Cn are determined.
Źródło:
Discussiones Mathematicae Graph Theory; 2018, 38, 2; 351-370
2083-5892
Pojawia się w:
Discussiones Mathematicae Graph Theory
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Every graph is local antimagic total and its applications
Autorzy:
Lau, Gee-Choon
Schaffer, Karl
Shiu, Wai-Chee
Powiązania:
https://bibliotekanauki.pl/articles/29519430.pdf
Data publikacji:
2023
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
local antimagic (total) chromatic number
Cartesian product
join product
Opis:
Let $ G = (V, E) $ be a simple graph of order $ p $ and size $ q $. A graph $ G $ is called local antimagic (total) if $ G $ admits a local antimagic (total) labeling. A bijection $ g : E → {1, 2, . . . , q} $ is called a local antimagic labeling of $ G $ if for any two adjacent vertices $ u $ and $ v $, we have $g^+(u) ≠ g^+(v) $, where $ g^+(u) = \Sigma_{e∈E(u)} g(e) $, and $ E(u) $ is the set of edges incident to $ u $. Similarly, a bijection $f : V (G)∪E(G) → {1, 2, . . . , p+q} $ is called a local antimagic total labeling of $ G $ if for any two adjacent vertices $ u $ and $ v $, we have $ w_f (u) ≠ w_f (v) $, where $ w_f (u) = f(u) + \Sigma_{e∈E(u)} f(e) $. Thus, any local antimagic (total) labeling induces a proper vertex coloring of $ G $ if vertex $ v $ is assigned the color $ g^+ (v) $ (respectively, $ w_f (u) $). The local antimagic (total) chromatic number, denoted $ χ_{la} (G) $ (respectively $ χ_{lat} (G)$ ), is the minimum number of induced colors taken over local antimagic (total) labeling of $ G $. We provide a short proof that every graph $ G $ is local antimagic total. The proof provides sharp upper bound to $ χ_{lat} (G) $. We then determined the exact $ χ_{lat} (G) $, where $ G $ is a complete bipartite graph, a path, or the Cartesian product of two cycles. Consequently, the $ χ_{la} (G ∨ K_1) $ is also obtained. Moreover, we determined the $ χ_{la} (G ∨ K_1) $ and hence the $χ_{lat} (G) $ for a class of 2-regular graphs $ G $ (possibly with a path). The work of this paper also provides many open problems on $ χ_{lat} (G) $. We also conjecture that each graph $ G $ of order at least 3 has $ χ_{lat} (G) ≤ χ_{la} (G) $.
Źródło:
Opuscula Mathematica; 2023, 43, 6; 841-864
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Model checking processes specified in join-calculus algebra
Autorzy:
Maludziński, S.
Dobrowolski, G.
Powiązania:
https://bibliotekanauki.pl/articles/305715.pdf
Data publikacji:
2014
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
join-calculus
model checking
formal methods
automatic software verification
Opis:
This article presents a model checking tool used to verify concurrent systems specified in join-calculus algebra. The temporal properties of systems under verification are expressed in CTL logic. Join-calculus algebra, with its operational semantics defined by a chemical abstract machine, serves as the basic method for the specification of concurrent systems and their synchronization mechanisms, allowing for the examination of more complex systems. The described model checker is a proof of concept for the utilization of new methodologies of formal system specification and verification in software engineering practice.
Źródło:
Computer Science; 2014, 15 (1); 61-74
1508-2806
2300-7036
Pojawia się w:
Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the special context of independent sets
Autorzy:
Slezák, Vladimír
Powiązania:
https://bibliotekanauki.pl/articles/728756.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
context
complete lattice
join-independent and meet-independent sets
Opis:
In this paper the context of independent sets $J^{p}_{L}$ is assigned to the complete lattice (P(M),⊆) of all subsets of a non-empty set M. Some properties of this context, especially the irreducibility and the span, are investigated.
Źródło:
Discussiones Mathematicae - General Algebra and Applications; 2001, 21, 1; 115-122
1509-9415
Pojawia się w:
Discussiones Mathematicae - General Algebra and Applications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the crossing numbers of join products of $W_4 + P_n$ and $W_4 + C_n$
Autorzy:
Stas, Michal
Valiska, Juraj
Powiązania:
https://bibliotekanauki.pl/articles/1397319.pdf
Data publikacji:
2021
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
graph
crossing number
join product
cyclic permutation
path
cycle
Opis:
The crossing number cr(G) of a graph G is the minimum number of edge crossings over all drawings of G in the plane. The main aim of the paper is to give the crossing number of the join product $W_4 + P_n$ and $W_4 + C_n$ for the wheel $W_4$ on five vertices, where $P_n$ and $C_n$ are the path and the cycle on n vertices, respectively. Yue et al. conjectured that the crossing number of $W_m + C_n$ is equal to $Z(m+1)Z(n)+(Z(m)-1)[n/2]+n+[m/2]+2$, for all m,n ≥ 3, and where the Zarankiewicz’s number $Z(n)=[n/2][{n-1}/2]$ is defined for n ≥ 1. Recently, this conjecture was proved for $W_3 + C_n$ by Klesc. We establish the validity of this conjecture for $W_4 + C_n$ and we also offer a new conjecture for the crossing number of the join product $W_m + P_n$ for m ≥ 3 and n ≥ 2.
Źródło:
Opuscula Mathematica; 2021, 41, 1; 95-112
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 37

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