Graphs with doubly resolving number 2

Abstract

Two vertices u,v in a connected graph G are doubly resolved by x,y∈G if d(v,x)−d(u,x)≠d(v,y)−d(u,y).A set W of vertices of the graph G is a doubly resolving set for G if every two distinct vertices of G are doubly resolved by some two vertices of W. Doubly resolving number of a graph G, denoted by ψ(G), is the minimum cardinality of a doubly resolving set for the graph G. In this paper all graphs G with ψ(G)=2 are characterized by using 2-connected subgraphs of G. © 2023 Elsevier B.V.