On the strong metric dimension of certain nanostructures

Let G(V , E) be a connected graph. A vertex w strongly resolves a pair of vertices u, v in V if there exists some shortest u-w path containing v or some shortest v -w path containing u. A set W ⊂ V of vertices is called a strong resolving set for G if every pair of vertices of V \W is strongly resolved by some vertex of W. A strong resolving set of minimum cardinality is called a strong metric basis and this cardinality is called the strong metric dimension of G. The strong metric dimension problem is to find a strong metric basis in a graph. In this paper we investigate the strong metric dimension problem for certain nanostructures.