On 2-Resolving Hop Dominating Sets in the Join, Corona and Lexicographic Product of Graphs

Authors

  • Angelica Mae Mahistrado MSU-IIT
  • Helen Rara

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i4.4585

Keywords:

2-resolving hop dominating set, 2-resolving hop domination number, join, corona, lexicographic product

Abstract

Let G be a connected graph. A set S of vertices in G is a 2-resolving hop dominating set of G if S is a 2-resolving set in G and for every vertex x ∈ V (G)\S there exists y ∈ S such that dG(x, y) = 2. The minimum cardinality of a set S is called the 2-resolving hop domination number of G and is denoted by γ2Rh(G). This study aims to combine the concept of hop domination with the 2-resolving sets of graphs. The main results generated in this study include the characterization of 2-resolving hop dominating sets in the join, corona and lexicographic product of two graphs, as well as their corresponding bounds or exact values.

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Published

2022-10-31

Issue

Vol. 15 No. 4: (October 2022)

Section

Nonlinear Analysis

License

Copyright (c) 2022 European Journal of Pure and Applied Mathematics

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How to Cite

On 2-Resolving Hop Dominating Sets in the Join, Corona and Lexicographic Product of Graphs. (2022). European Journal of Pure and Applied Mathematics, 15(4), 1982-1997. https://doi.org/10.29020/nybg.ejpam.v15i4.4585