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 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.