2-Locating Sets in a Graph
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Published:2023-07-30
Issue:3
Volume:16
Page:1647-1662
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ISSN:1307-5543
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Container-title:European Journal of Pure and Applied Mathematics
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language:
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Short-container-title:Eur. J. Pure Appl. Math.
Author:
Canete Gymaima,Rara Helen,Mahistrado Angelica Mae
Abstract
Let $G$ be an undirected graph with vertex-set $V(G)$ and edge-set $E(G)$, respectively. A set $S\subseteq V(G)$ is a $2$-locating set of $G$ if $\big|[\big(N_G(x)\backslash N_G(y)\big)\cap S] \cup [\big(N_G(y)\backslash N_G(x)\big)\cap S]\big|\geq 2$, for all \linebreak $x,y\in V(G)\backslash S$ with $x\neq y$, and for all $v\in S$ and $w\in V(G)\backslash S$, $\big(N_G(v)\backslash N_G(w)\big)\cap S \neq \varnothing$ or $\big(N_G(w)\backslash N_G[v]\big) \cap S\neq \varnothing$. In this paper, we investigate the concept and study 2-locating sets in graphs resulting from some binary operations. Specifically, we characterize the 2-locating sets in the join, corona, edge corona and lexicographic product of graphs, and determine bounds or exact values of the 2-locating number of each of these graphs.
Funder
Department of Science and Technology, Republic of the Philippines
Publisher
New York Business Global LLC
Subject
Applied Mathematics,Geometry and Topology,Numerical Analysis,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science