On the local metric dimension of corona product graphs

Abstract

A vertex $v\in V(G)$ is said to distinguish two vertices $x,y\in V(G)$ of a nontrivial connected graph $G$ if the distance from $v$ to $x$ is different from the distance from $v$ to $y$. A set $S\subset V(G)$ is a local metric generator for $G$ if every two adjacent vertices of $G$ are distinguished by some vertex in $S$. 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. In this paper we study the problem of finding exact values for the local metric dimension of corona product of graphs.