Abstract |
Let G be a connected graph. An ordered set of vertices {v1, ...,vl} is a 2-resolving set
in G if, for any distinct vertices u, w in V (G), the lists of distances (dG(u, v1),..., dG(u; vl)) and
(dG(w, v1),..., dG(w; vl)) differ in at least 2 positions. If G has a 2-resolving set, we denote the
least size of a 2-resolving set by dim2(G), the 2-metric dimension of G. A 2-resolving set of size
dim2(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 determines the
exact values of the 2-metric dimension of these graphs. |