TY - JOUR
AU - Canete, Gymaima
AU - Rara, Helen
AU - Mahistrado, Angelica Mae
PY - 2023/07/30
Y2 - 2023/11/29
TI - 2-Locating Sets in a Graph
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 16
IS - 3
SE -
DO - 10.29020/nybg.ejpam.v16i3.4821
UR - https://ejpam.com/index.php/ejpam/article/view/4821
SP - 1647-1662
AB - <p>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 $x
eq y$, and for all $v\in S$ and $w\in V(G)\backslash S$, $\big(N_G(v)\backslash N_G(w)\big)\cap S
eq \varnothing$ or $\big(N_G(w)\backslash N_G[v]\big) \cap S
eq \varnothing$. 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.</p>
ER -