Results 11 to 20 of about 2,463 (224)
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 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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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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On the Gonality of Cartesian Products of Graphs [PDF]
The Electronic Journal of Combinatorics, 2020 In this paper we provide the first systematic treatment of Cartesian products of graphs and their divisorial gonality, which is a tropical version of the gonality of an algebraic curve defined in terms of chip-firing. We prove an upper bound on the gonality of the Cartesian product of any two graphs, and determine instances where this bound holds with
Ivan Aidun, Ralph Morrison
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On Cartesian Products of Signed Graphs [PDF]
Discrete Applied Mathematics, 2020 In this paper, we study the Cartesian product of signed graphs as defined by Germina, Hameed and Zaslavsky (2011). Here we focus on its algebraic properties and look at the chromatic number of some Cartesian products. One of our main results is the unicity of the prime factor decomposition of signed graphs.
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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.
Martin Kreh, Jan-Hendrik de Wiljes
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The Cartesian product of graphs with loops
Ars Mathematica Contemporanea, 2015 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 unlooped vertex. We also prove that this factorization can be computed in O(m) time, where m is the number
Tetiana Boiko +4 more
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