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Betweenness centrality in Cartesian product of graphs [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 Betweenness centrality is a widely used measure in various graphs and it has a pivotal role in the analysis of complex networks. It measures the potential or power of a node to control the communication over the network.
Sunil Kumar R., Kannan Balakrishnan
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On linkedness in the Cartesian product of graphs [PDF]
Periodica Mathematica Hungarica, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gabor Mészáros
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Connectivity of Cartesian product graphs
Discrete Mathematics, 2006 Let \(n(G)\), \(\kappa(G)\), \(\lambda(G)\) and \(\delta(G)\) be the order, connectivity, edge-connectivity and minimum degree of a (di-)graph, respectively. In addition, let \(G_1\times G_2\) be the Cartesian product of two (di-)graphs \(G_1\) and \(G_2\). If \(G_1,G_2\) are two connected graphs, then the authors prove that \(\kappa(G_1\times G_2)\geq\
Jun-Ming Xu, Chao Yang
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On Path-Pairability in the Cartesian Product of Graphs
Discussiones Mathematicae Graph Theory, 2016 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.
Mészáros Gábor
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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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On subgraphs of Cartesian product graphs
Discrete Mathematics, 2002 All graphs considered are finite undirected and simple ones. Such graphs which can be represented as nontrivial subgraphs of Cartesian product graphs are characterized. In general a graph \(G\) is prime with respect to a graph product \(*\) if it cannot be represented as a product of two nontrivial graphs, and \(G\) is called \(S\)-prime with respect ...
Sandi Klavžar +2 more
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The Thickness of Amalgamations and Cartesian Product of Graphs
Discussiones Mathematicae Graph Theory, 2017 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 ...
Yang Yan, Chen Yichao
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On Total Domination in the Cartesian Product of Graphs
Discussiones Mathematicae Graph Theory, 2018 Ho proved in [A note on the total domination number, Util. Math. 77 (2008) 97–100] that the total domination number of the Cartesian product of any two graphs without isolated vertices is at least one half of the product of their total domination numbers.
Brešar Boštjan +3 more
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Motion planning in cartesian product graphs
Discussiones Mathematicae Graph Theory, 2014 Let G be an undirected graph with n vertices. Assume that a robot is placed on a vertex and n − 2 obstacles are placed on the other vertices. A vertex on which neither a robot nor an obstacle is placed is said to have a hole.
Deb Biswajit, Kapoor Kalpesh
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Molecules, 2018 The Cartesian product and join are two classical operations in graphs. Let dL(G)(e) be the degree of a vertex e in line graph L(G) of a graph G. The edge versions of atom-bond connectivity (ABCe) and geometric arithmetic (GAe) indices of G are defined as
Xiujun Zhang +3 more
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