Results 11 to 20 of about 59,909 (247)
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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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\
Xu, Jun-Ming, Yang, Chao
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The Cartesian product of graphs with loops [PDF]
Ars Mathematica Contemporanea, 2014 We extend the definition of the Cartesian product to graphs with loops and show that the Sabidussi-Vizing unique factorization theorem for connected finite simple graphs still holds in this context for all connected finite graphs with at least one ...
Christiaan E. Van De Woestijne +7 more
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Hadwiger Number and the Cartesian Product Of Graphs [PDF]
Graphs and Combinatorics, 2007 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.
Chandran, L. Sunil +2 more
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Power domination of the cartesian product of graphs
AKCE International Journal of Graphs and Combinatorics, 2016 In this paper, we first give a brief survey on the power domination of the Cartesian product of graphs. Then we conjecture a Vizing-like inequality for the power domination problem, and prove that the inequality holds when at least one of the two graphs ...
K.M. Koh, K.W. Soh
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Connectivity of Cartesian products of graphs
Applied Mathematics Letters, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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DP‐coloring Cartesian products of graphs
Journal of Graph Theory, 2022 AbstractDP‐coloring (also called correspondence coloring) is a generalization of list coloring introduced by Dvořák and Postle in 2015. Motivated by results related to list coloring Cartesian products of graphs, we initiate the study of the DP‐chromatic number, , of the same. We show that , where is the coloring number of the graph .
Hemanshu Kaul +3 more
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Peg Solitaire on Cartesian Products of Graphs [PDF]
Graphs and Combinatorics, 2021 AbstractIn 2011, Beeler and Hoilman generalized the game of peg solitaire to arbitrary connected graphs. In the same article, the authors proved some results on the solvability of Cartesian products, given solvable or distance 2-solvable graphs. We extend these results to Cartesian products of certain unsolvable graphs.
Kreh, Martin, Wiljes, Jan-Hendrik de
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Nonseparating Independent Sets of Cartesian Product Graphs [PDF]
Taiwanese Journal of Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Cao, Fayun, Ren, Han
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