Abstract
Consider a simple connected undirected graph G = (V, E), where V represents the vertex set and E represents the edge set, respectively. A subset D of V is called doubly resolving set if for every two vertices x, y of G, there are two vertices u, v is an element of D such that d(u, x) - d(u; y) not equal d(v, x) - d(v, y). A doubly resolving set with minimum cardinality is called minimal doubly resolving set. This minimum cardinality is denoted by psi(G).
In this paper, we find the minimal doubly resolving set for necklace graph N-en, n >= 2. Also, we prove that psi(N-en) = 3 for n >= 2.