On the local fractional metric dimension of corona product graphs

Abstract

A vertex in a connected graph is said to resolve a pair of vertices {u, v} in if the distance from to is not equal to the distance from v to x. A set of vertices of is a resolving set for G if every pair of vertices is resolved by some vertices of S. The smallest cardinality of a resolving set for G is called the metric dimension of G, denoted by dim(G). For the pair of two adjacent vertices {u, v} is called the local resolving neighbourhood and denoted by R 1{u, v}. A real valued function g 1: V(G) → [0,1] is a local resolving function of G if for every two adjacent vertices u, v ∈ V(G). The local fractional metric dimension of G is defined as dimft(G) = min{|g 1|: g 1 is local resolving function of G} where |g 1| = ∑v∈V g 1(v). Let and be two graphs of order n 1 and n 2, respectively. The corona product Go H is defined as the graph obtained from G and H by taking one copy of G and n 1 copies of H and joining by an edge each vertex from the ith -copy of H with the ith -vertex of G. In this paper we study the problem of finding exact values for the fractional local metric dimension of corona product of graphs.