Restrained Disjunctive Domination in Graphs under Some Binary Operations

Authors

  • Rolando Penafiel Malalay Zamboanga Peninsula Polytechnic State University http://orcid.org/0000-0003-2786-2965
  • Ferdinand Paler Jamil Mindanao State University-Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i1.4187

Keywords:

Disjunctive dominating set, restrained disjunctive dominating set, restrained disjunctive domination number, join, corona and lexicographic product

Abstract

A set S ⊆ V (G) is a disjunctive dominating set of a graph G if for every v ∈ V (G)\S, v is a neighbor of a vertex in S or S has at least two vertices each at distance 2 from v. We say that a disjunctive dominating set S of G is a restrained disjunctive dominating set if for each v ∈ V (G)\S there exists u ∈ V (G) \ S such that uv ∈ E(G) or there exist distinct vertices u, w ∈ V (G) \ S such that dG(u, v) = 2 = dG(w, v). The minimum cardinality γdr(G) of a restrained disjunctive dominating set of G is the restrained disjunctive domination number of G. In this paper, we characterize the restrained disjunctive dominating sets in some binary operations such as the join, corona and lexicographic product of graphs and, as a result, obtain the values of their corresponding restrained disjunctive domination numbers.

Author Biographies

  • Rolando Penafiel Malalay, Zamboanga Peninsula Polytechnic State University
    College of Engineering and Technology, Instructor 1
  • Ferdinand Paler Jamil, Mindanao State University-Iligan Institute of Technology
    Department of Mathematics and Statistics, College of Science and Mathematics, Center of Graph Theory, Algebra and Analysis-Premier Research Institute of Science and Mathematics, Professor VI

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Published

2022-01-31

Issue

Section

Nonlinear Analysis

How to Cite

Restrained Disjunctive Domination in Graphs under Some Binary Operations. (2022). European Journal of Pure and Applied Mathematics, 15(1), 207-223. https://doi.org/10.29020/nybg.ejpam.v15i1.4187