Local metric dimension of circulant graph circ(n:1,2,…,n+12)

Let G be a connected graph with two vertices u and v. The distance between u and v, denoted by d(u, v), is defined as length of the shortest path from u to v in G. For an ordered set W = {w1, w2, w3, … , wk} of k distinct vertices in a nontrivial connected graph G, the representation of a vertex v of V(G) respect to W is r(v|W) = (d(v, w1), d(v, w2), … , d(v, wk)). The set W is a resolving set of G if r(v|W) for each vertex v ∈ V(G) is distinct. A resolving set of minimum cardinality is a metric dimension and denoted by dim(G). The set W is a local resolving set of G if r(v|W) for every two adjacent vertices of V(G) is distinct. The minimum cardinality of local resolving set of G is a local metric dimension and denoted by ldim(G). In this research, we determine local metric dimension of circulant graph circ(n:1,2,3,…,n+12).