A dominating set  is called an equitable dominating set if for every vertex  there exists a vertex  such that  The distance  between two vertices in G is the length of the shortest path between u and v in G. Let be an ordered subset of V(G) and let v ∈ V(G). Then the k-vector  is called the resolving vector of v with respect to W and is denoted by  The set W is called a resolving set of G if  for any two distinct vertices u and v. A set  is called a resolving dominating set if it is resolving and dominating both. A dominating set D is called an equitable resolving dominating set if it is resolving as well as equitable. The minimum cardinality of an equitable resolving dominating set is called an equitable resolving domination number of G, denoted by  In the present work, some characterizations are established and equitable resolving domination numbers for various graphs are investigated.

dominating set, equitable dominating set, resolving set, metric dimension, equitable resolving dominating set, equitable resolving domination number.

Received: September 26, 2022; Revised: February 2, 2023; Accepted: February 14, 2023; Published: February 17, 2023

How to cite this article: S. K. Vaidya and J. B. Kelaiya, Equitable resolving dominating sets in graphs, Advances and Applications in Discrete Mathematics 38(1) (2023), 15-28. http://dx.doi.org/10.17654/0974165823016

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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