Doubly resolving number of the corona product graphs - Jannesari, Mohsen (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2025)
Two vertices u, v in a connected graph G are doubly resolved by vertices x, y of 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 G. In this paper, using adjacency resolving sets and dominating sets of graphs, we study doubly resolving sets in the corona product of graphs G and H, G ⊙ H. First, we obtain the upper and lower bounds for the doubly resolving number of the corona product G ⊙ H in terms of the order of G and the adjacency dimension of H, then we present several conditions that make each of these bounds feasible for the doubly resolving number of G ⊙ H. Also, for some important families of graphs, we obtain the exact value of the doubly resolving number of the corona product.