Graphs with doubly resolving number 2

Two vertices u, v in a connected graph G are doubly resolved by x, y E 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 *(G), is the minimum cardinality of a doubly resolving set for the graph G. In this paper all graphs G with *(G) = 2 are characterized by using 2-connected subgraphs of G.& COPY; 2023 Elsevier B.V. All rights reserved.