The Local Metric Dimension of Strong Product Graphs

Abstract

A vertex $$v\in V(G)$$v?V(G) is said to distinguish two vertices $$x,y\in V(G)$$x,y?V(G) of a nontrivial connected graph G if the distance from v to x is different from the distance from v to y. A set $$S\subset V(G)$$S?V(G) is a local metric generator for G if every two adjacent vertices of G are distinguished by some vertex of S. A local metric generator with the minimum cardinality is called a local metric basis for G and its cardinality, the local metric dimension of G. It is known that the problem of computing the local metric dimension of a graph is NP-Complete. In this paper we study the problem of finding exact values or bounds for the local metric dimension of strong product of graphs.