Closed formulae for the strong metric dimension of lexicographic product graphs
Dorota Kuziak, Juan Alberto Rodriguez-Velazquez, González Ismael Yero · Discussiones Mathematicae Graph Theory · 2016
Given a connected graph G, a vertex w V (G) strongly resolves two vertices u, v V (G) if there exists some shortest uw path containing v or some shortest vw path containing u. A set S of vertices is a strong metric generator for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong metric generator for G is called the strong metric dimension of G. In this paper we obtain several relationships between the strong metric dimension of the lexicographic product of graphs and the strong metric dimension of its factor graphs.