Strictly Locating Sets in a Graph

Abstract

Let $G$ be a connected graph. A subset $S$ of $V(G)$ is a locating set in $G$ if for all $u,v\in V(G)\backslash S$, $N_{G}(u)\cap S\neq N_{G}(v)\cap S$. A subset $S$ of $V(G)$ is a strictly locating set in $G$ if $S$ is a locating set in $G$ and $N_{G}(w)\cap S\neq S$ $\forall w\in V(G)\backslash S$. The minimum cardinality of a strictly locating set in $G$, denoted by $sln(G)$, is called the strictly locating number of $G$. In this paper, the concept of strictly locating set in a graph is investigated. Moreover, the strictly locating sets in the join and corona of graphs are characterized and the strictly locating numbers of these graphs are determined.