Revisiting Domination, Hop Domination, and Global Hop Domination in Graphs

Authors

  • Gemma Puebla Salasalan Davao del Sur State College
  • Sergio R Canoy, Jr Mindanao State University - Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i4.4144

Keywords:

domination, hop domination, global hop domination, complementary prism, shadow graph

Abstract

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. It is a global hop dominating set of G if it is a hop dominating set of both G and the complement  of G. The minimum cardinality of a hop dominating (global hop dominating) set of G, denoted by γh(G)(resp.γgh(G))
, is called the hop domination (resp. global hop domination) number of G. In this paper, we give some realization results involving domination, hop domination, and global hop domination parameters. Also, we give a rectification of a result found in a recent paper of the authors and use this to prove some results in this paper.

 

 

Author Biographies

  • Gemma Puebla Salasalan, Davao del Sur State College
    Department of Arts and Sciences, Instructor
  • Sergio R Canoy, Jr, Mindanao State University - Iligan Institute of Technology
    Department of Mathematics and Statistics, Professor

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Published

2021-11-10

Issue

Vol. 14 No. 4: (October 2021)

Section

Nonlinear Analysis

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How to Cite

Revisiting Domination, Hop Domination, and Global Hop Domination in Graphs. (2021). European Journal of Pure and Applied Mathematics, 14(4), 1415-1428. https://doi.org/10.29020/nybg.ejpam.v14i4.4144