The Local (Adjacency) Metric Dimension of Split Related Complete Graph

Abstract

Let G be a simple graph. A set of vertices, called V (G) and a set of edges, called E(G) are two sets which form graph G. W is a local adjacency resolving set of G if for every two distinct vertices x, y and x adjacent with y then rA(x|W) 6= rA(y|W). A minimum local adjacency resolving set in G is called local adjacency metric basis. The cardinality of vertices in the basis is a local adjacency metric dimension of G (dimA,l(G)). We present the exact value of local adjacency metric dimension of m-splitting complete and bipartite graphs