On Local Adjacency Metric Dimension of Some Wheel Related Graphs with Pendant Points

Abstract

Let G =(V(G),E(G)) be any connected graph of order n = |V(G)| and measure m = |E(G)|. For an order set of vertices S = { s 1 , s 2 , ..., s k } and a vertex v in G, the adjacency representation of v with respect to S is the ordered k- tuple r A (v|S) = (d A (v, s 1 ), d A (v, s 2 ), ..., d A (v, s k )), where d A (u,v) represents the adjacency distance between the vertices u and v. The set S is called a local adjacency resolving set of G if for every two distinct vertices u and v in G, u adjacent v then r A (u|S) ≠ r A (v|S) . A minimum local adjacency resolving set for G is a local adjacency metric basis of G. Local adjacency metric dimension for G, dim A,l (G), is the cardinality of vertices in a local adjacency metric basis for G.