On 2-Resolving Sets in the Join and Corona of Graphs

Let G be a connected graph. An ordered set of vertices {v(1) , ..., v(l)} is a 2-resolving set in G if, for any distinct vertices u, w is an element of V(G), the lists of distances (d(G)(u,v(1)), ...,d(G)(u, v(l))) and (d(G)(w, v(1)), ..., d(G)(w, v(l))) differ in at least 2 positions. If G has a 2-resolving set, we denote the least size of a 2-resolving set by dim(2) (G), the 2-metric dimension of G. A 2-resolving set of size dim(2) (G) is called a 2-metric basis for G. This study deals with the concept of 2-resolving set of a graph. It characterizes the 2-resolving set in the join and corona of graphs and determine the exact values of the 2-metric dimension of these graphs.