Hop Differentiating Hop Dominating Sets in Graphs

Authors

  • Sergio Canoy, Jr.
  • Chrisley Jade Saromines Mindanao State University - Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v16i1.4673

Keywords:

Hop domination, Join, corona and lexicographic product

Abstract

A subset S of V (G), where G is a simple undirected graph, is hop dominating if for each v ∈ V (G) \ S, there exists w ∈ S such that dG(v, w) = 2 and it is hop differentiating if N2 G[u] ∩ S ̸= N2 G[v] ∩ S for any two distinct vertices u, v ∈ V (G). A set S ⊆ V (G) is hop differentiating hop dominating if it is both hop differentiating and hop dominating in G. The minimum cardinality of a hop differentiating hop dominating set in G, denoted by γdh(G), is called the hop differentiating hop domination number of G. In this paper, we investigate some properties of this newly defined parameter. In particular, we characterize the hop differentiating hop dominating sets in graphs under some binary operations.

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Published

2023-01-29

Issue

Vol. 16 No. 1: (January 2023)

Section

Nonlinear Analysis

License

Copyright (c) 2023 European Journal of Pure and Applied Mathematics

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How to Cite

Hop Differentiating Hop Dominating Sets in Graphs. (2023). European Journal of Pure and Applied Mathematics, 16(1), 440-453. https://doi.org/10.29020/nybg.ejpam.v16i1.4673