Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 13, No 1 (2025): Electronic Journal of Graph Theory and Applications

Doubly resolving number of the corona product graphs

Jannesari, Mohsen (‎University of Isfahan)



Article Info

Publish Date
01 May 2025

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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Journal Info

Abbrev

ejgta

Publisher

Subject

Electrical & Electronics Engineering

Description

The Electronic Journal of Graph Theory and Applications (EJGTA) is a refereed journal devoted to all areas of modern graph theory together with applications to other fields of mathematics, computer science and other sciences. The journal is published by the Indonesian Combinatorial Society ...