Results 31 to 40 of about 3,577 (286)
The Forcing Domination Number of Hamiltonian Cubic Graphs [PDF]
, 2009 The authors presented a sequence of Hamiltonian cubic graphs whose domination numbers are sharp and in this paper we study forcing domination number for those ...
H. Abdollahzadeh Ahangar +3 more
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Generalized 3-edge-connectivity of Cartesian product graphs [PDF]
, 2015 summary:The generalized $k$-connectivity $\kappa _{k}(G)$ of a graph $G$ was introduced by Chartrand et al. in 1984. As a natural counterpart of this concept, Li et al.
Sun, Yuefang
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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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On star coloring of degree splitting of cartesian product graphs
, 2022 A star coloring of a graph G is a proper vertex coloring with the condition that no path on four vertices in G can be labelled by two colors. The star chromatic number chi(s) (G) of G is the least number of colors that is required to star color G.
Ulagammal, S., Vivin, Vernold J.
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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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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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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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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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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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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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