Results 21 to 30 of about 2,463 (224)
Hadwiger Number and the Cartesian Product of Graphs [PDF]
Graphs and Combinatorics, 2008 The Hadwiger number mr(G) of a graph G is the largest integer n for which the complete graph K_n on n vertices is a minor of G. Hadwiger conjectured that for every graph G, mr(G) >= chi(G), where chi(G) is the chromatic number of G. In this paper, we study the Hadwiger number of the Cartesian product G [] H of graphs.
Chandran, L Sunil +2 more
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Geodesic bipancyclicity of the Cartesian product of graphs
Theory and Applications of Graphs, 2022 A cycle containing a shortest path between two vertices $u$ and $v$ in a graph $G$ is called a $(u,v)$-geodesic cycle. A connected graph $G$ is geodesic 2-bipancyclic, if every pair of vertices $u,v$ of it is contained in a $(u,v)$-geodesic cycle of ...
Amruta Shinde, Y.M. Borse
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On the connectivity of Cartesian product of graphs
Ars Mathematica Contemporanea, 2013 We give a new alternative proof of Liouville’s formula which states that for any graphs G and H on at least two vertices, κ ( G □ H ) = min{ κ ( G )| H |, | G | κ ( H ), δ ( G ) + δ ( H )} , where κ and δ denote the connectivity number and minimum degree of a given graph, respectively.
Jelena Govorcin, Riste Skrekovski
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On the Skew Spectra of Cartesian Products of Graphs [PDF]
The Electronic Journal of Combinatorics, 2013 An oriented graph ${G^{\sigma}}$ is a simple undirected graph $G$ with an orientation, which assigns to each edge of $G$ a direction so that ${G^{\sigma}}$ becomes a directed graph. $G$ is called the underlying graph of ${G^{\sigma}}$ and we denote by $S({G^{\sigma}})$ the skew-adjacency matrix of ${G^{\sigma}}$ and its spectrum $Sp({G^{\sigma}})$ is ...
Denglan Cui, Yaoping Hou
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On primality of Cartesian product of graphs [PDF]
Arab Journal of Mathematical SciencesPurposeThe present work focuses on the primality and the Cartesian product of graphs.Design/methodology/approachGiven a graph G, a subset M of V (G) is a module of G if, for a, b ∈ M and x ∈ V (G) \ M, xa ∈ E(G) if and only if xb ∈ E(G).
Nadia El Amri +2 more
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GRACEFUL CHROMATIC NUMBER OF SOME CARTESIAN PRODUCT GRAPHS
Ural Mathematical Journal, 2023 A graph \(G(V,E)\) is a system consisting of a finite non empty set of vertices \(V(G)\) and a set of edges \(E(G)\). A (proper) vertex colouring of \(G\) is a function \(f:V(G)\rightarrow \{1,2,\ldots,k\},\) for some positive integer \(k\) such that ...
I Nengah Suparta +3 more
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Prime Factorization And Domination In The Hierarchical Product Of Graphs
Discussiones Mathematicae Graph Theory, 2017 In 2009, Barrière, Dalfó, Fiol, and Mitjana introduced the generalized hierarchical product of graphs. This operation is a generalization of the Cartesian product of graphs.
Anderson S.E. +3 more
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The adjacency spectrum of two new operations of graphs
AKCE International Journal of Graphs and Combinatorics, 2018 Let be a graph and be its adjacency matrix. The eigenvalues of are the eigenvalues of and form the adjacency spectrum, denoted by . In this paper, we introduce two new operations and , and describe the adjacency spectra of and of regular graphs , and ...
Dijian Wang, Yaoping Hou, Zikai Tang
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The profile of the Cartesian product of graphs
Discrete Applied Mathematics, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
David Kuo, Jing-Ho Yan
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On the Metric Dimension of Cartesian Products of Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2007 A set S of vertices in a graph G resolves G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. This paper studies the metric dimension of cartesian products G*H.
José Cáceres +6 more
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