Strong metric dimension of generalized Jahangir graph

Abstract

Let $G$ be a simple and connected graph with vertex set $V(G)$. A vertex $w\in V(G)$ strongly resolves two vertices $u,v\in V(G)$ if $v$ belongs to a shortest $u-w$ path or $u$ belongs to a shortest $v-w$ path. A set $W\subseteq V(G)$ is a strong resolving set for $G$ if every pair of vertices of $G$ is strongly resolved by some vertex of $W$. A strong metric basis of $G$ is a strong resolving set for $G$ with minimum cardinality. The strong metric dimension of $G$, denoted by $sdim(G)$, is the cardinality of a strong metric basis of $G$. In this paper we compute the strong metric dimension of generalized Jahangir graph $J(n,m)$, where $m\ge 3$ and $n\ge 2$.