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

摘要

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= { si, s_2,...,sk} and a vertex v in G, the adjacency representation of v with respect to S is the ordered ktuple rA(v|S)= (dA(v, si), d_A(v, s_2),...,d_A(v, sk)), where dA(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 r4(U|S)≠rA(v|S) . A minimum local adjacency resolving set for G is a local adjacency metric basis of G. Local adjacency metric dimension for G, dinu,l(G), is the cardinality of vertices in a local adjacency metric basis for G. In this paper, we study and determine the local adjacency metric dimension of some wheel related graphs G (namely gear graph, helm, sunflower and friendship graph) with pendant points, that is edge corona product of G and a trivial graph K_1,G?K_1. Moreover, we compare among the local adjacency metric dimension of G?K_1 graph,of W_n ?K_1 graph and metric dimension of W n.