Local Metric Dimension of the Line Graph of a Generalized Petersen Graph

Let G be a graph that has a vertex set V(G) and an edge set E(G). Let W={w_1,w_2,…w_k} be a subset of V(G). The representation of a vertex v∈V(G) with respect to W, denoted by r(v|W), is defined as k-vector (d(v,w_1 ),d(v,w_2 ), …, d(v,w_k )). A set W is called a local resolving set of G if r(u│W)≠r(v│W) for every two adjacent vertices u,v∈V(G). The smallest cardinality of all local resolving set in G is called the local metric dimension of G, denoted by lmd(G). The local resolving set of G with cardinality lmd⁡(G) is called a local basis of G. In this paper, we determine the local metric dimension of the line graph of generalized Petersen graph P_(n,1).