2-Locating Sets in a Graph

Authors

  • Gymaima Canete MSU-IIT
  • Helen Rara MSU-IIT
  • Angelica Mae Mahistrado MSU-IIT

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i3.4821

Keywords:

2-locating set, 2-locating number, join, corona, edge corona, lexicographic product

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.

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Published

2023-07-30

Issue

Section

Nonlinear Analysis

How to Cite

2-Locating Sets in a Graph. (2023). European Journal of Pure and Applied Mathematics, 16(3), 1647-1662. https://doi.org/10.29020/nybg.ejpam.v16i3.4821

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