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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Jannesari, Mohsen
‎University of Isfahan
Electrical & Electronics Engineering

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Doubly resolving number of the corona product graphs Jannesari, Mohsen
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 1 (2025): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2025.13.1.15

Abstract

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. 
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