Abstract

Let G be a connected graph with vertex set V (G) and edge set E(G). For every pair of vertices u, v ∈ V (G), the interval I[u, v] between u and v to be the collection of all vertices that belong to some shortest u−v path. A vertex s ∈ V (G) strongly resolves two vertices u and v if u belongs to a shortest v − s path or v belongs to a shortest u − s path. A vertex set S of G is a strong resolving set of G if every two distinct vertices of G are strongly resolved by some vertex of S. The strong metric basis of G is a strong resolving set with minimal cardinality. The strong metric dimension sdim(G) of a graph G is defined as the cardinality of strong metric basis. In this paper we determine the strong metric dimension of a broken fan graph, starbarbell graph, and Cm ?k Pn graph. Keywords : strong metric dimension, strongly resolved set, broken fan graph, starbarbell graph, Cm ?k Pn graph