Hop Dominating Sets in Graphs Under Binary Operations

Authors

  • Sergio Canoy, Jr Mindanao State University-Iligan Institute of Technology
  • Reynaldo Villarobe Mollejon Visayas State University-Villaba
  • John Gabriel E. Canoy

DOI:

https://doi.org/10.29020/nybg.ejpam.v12i4.3550

Keywords:

domination, hop domination, join, corona, and lexicographic product

Abstract

Let G be a (simple) connected graph with vertex and edge sets V (G) and E(G),
respectively. A set S ⊆ V (G) is a hop dominating set of G if for each v ∈ V (G) \ S, there exists w ∈ S such that dG(v, w) = 2. The minimum cardinality of a hop dominating set of G, denoted by γh(G), is called the hop domination number of G. In this paper we revisit the concept of hop domination, relate it with other domination concepts, and investigate it in graphs resulting from some binary operations.

Author Biography

  • Reynaldo Villarobe Mollejon, Visayas State University-Villaba
    Department of Teacher Education, Assistant Professor 1

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Published

2019-10-31

Issue

Section

Nonlinear Analysis

How to Cite

Hop Dominating Sets in Graphs Under Binary Operations. (2019). European Journal of Pure and Applied Mathematics, 12(4), 1455-1463. https://doi.org/10.29020/nybg.ejpam.v12i4.3550