Strong Resolving Hop Domination in Graphs

Authors

  • Jerson Mohamad Western Mindanao State University
  • Helen Rara

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i1.4578

Keywords:

strong resolving hop domination set, strong resolving hop domination number, hop dominated superclique, join, corona, lexicographic product

Abstract

A vertex w in a connected graph G strongly resolves two distinct vertices u and v in V (G) if v is in any shortest u-w path or if u is in any shortest v-w path. A set W of vertices in G is a strong resolving set G if every two vertices of G are strongly resolved by some vertex of W. A set S subset of V (G) is a strong resolving hop dominating set of G if S is a strong resolving set in G and for every vertex v ∈ V (G) \ S there exists u ∈ S such that dG(u, v) = 2. The smallest cardinality of such a set S is called the strong resolving hop domination number of G. This paper presents the characterization of the strong resolving hop dominating sets in the join, corona and lexicographic product of graphs. Furthermore, this paper determines the exact value or bounds of their corresponding strong resolving hop domination number.

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How to Cite

Mohamad, J., & Rara, H. (2023). Strong Resolving Hop Domination in Graphs. European Journal of Pure and Applied Mathematics, 16(1), 131–143. https://doi.org/10.29020/nybg.ejpam.v16i1.4578

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