Closed formulae for the strong metric dimension of lexicographic product graphs

Identifier:  imarina:5130478

Handle: https://hdl.handle.net/20.500.11797/imarina5130478

Authors:  Kuziak, Dorota; Yero, Ismael G; Rodriguez-Velazquez, Juan A

Abstract:
Given a connected graph G, a vertex w ¿ V(G) strongly resolves two vertices u,v ¿ V(G) if there exists some shortest u - w path containing v or some shortest v - w 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. © 2016, University of Zielona Gora.