Strong metric dimension of generalized Jahangir graph

TL;DR

This paper calculates the strong metric dimension of generalized Jahangir graphs, providing a precise measure of the minimum number of vertices needed to strongly resolve all pairs in these graphs.

Contribution

It introduces the computation of the strong metric dimension specifically for generalized Jahangir graphs, a novel contribution in graph theory.

Findings

Derived formulas for the strong metric dimension of $J(n,m)$

Extended understanding of resolving sets in complex graphs

Provided exact values for various parameters of generalized Jahangir graphs

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 $m\geq 3$ and $n\geq 2$.