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

Authors

  • Jean Mansanadez Cabaro Mindanao State University-Marawi
  • Helen Rara

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i3.4426

Keywords:

2-resolving set, 2-resolving dominating set, 2R-domination number, lexicographic product of two graphs

Abstract

Let G be a connected graph. An ordered set of vertices {v1, ..., vl} is a 2-resolving set for G if, for any distinct vertices u, w ∈ V (G), the lists of distances (dG(u, v1), ..., dG(u, vl)) and (dG(w, v1), ..., dG(w, vl)) differ in at least 2 positions. A 2-resolving set S ⊆ V (G) which is
dominating is called a 2-resolving dominating set or simply 2R-dominating set in G. The minimum cardinality of a 2-resolving dominating set in G, denoted by γ2R(G), is called the 2R-domination number of G. Any 2R-dominating set of cardinality γ2R(G) is then referred to as a γ2R-set in G. This study deals with the concept of 2-resolving dominating set of a graph. It characterizes the 2-resolving dominating set in the join, corona and lexicographic product of two graphs and determine the bounds or exact values of the 2-resolving dominating number of these graphs.

Author Biographies

  • Jean Mansanadez Cabaro, Mindanao State University-Marawi

    Faculty,Mathematics Department, College of Natural Sciences and Mathematics, Mindanao State
    University-Main Campus, 9700 Marawi City, Philippines

  • Helen Rara

    Department of Mathematics and Statistics, College of Science and Mathematics, Center of
    Graph Theory, Algebra, and Analysis-Premier Research Institute of Science and Mathemat-
    ics, Mindanao State University-Iligan Institute of Technology, 9200 Iligan City, Philippines

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Published

2022-07-31

Issue

Section

Nonlinear Analysis

How to Cite

On 2-Resolving Dominating Sets in the Join, Corona and Lexicographic Product of Two Graphs. (2022). European Journal of Pure and Applied Mathematics, 15(3), 1417-1425. https://doi.org/10.29020/nybg.ejpam.v15i3.4426

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