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

Authors

  • Jean M. Cabaro Mindanao State University-Marawi
  • Helen Rara

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i3.4427

Keywords:

restrained 2-resolving set, restrained 2-resolving dominating set, join, corona, 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 set S ⊆ V (G) is a restrained 2-resolving set in G if S is a 2-resolving set in G and S = V (G) or ⟨V (G)\S⟩ has no isolated vertex. The restrained 2-resolving number of G, denoted by rdim2(G), is the smallest cardinality of a restrained 2-resolving set in G. A restrained 2-resolving set of cardinality rdim2(G) is then referred to as an rdim2-set in G. This study deals with the concept of restrained 2-resolving set of a graph. It
characterizes the restrained 2-resolving 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 M. 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

Vol. 15 No. 3: (July 2022)

Section

Nonlinear Analysis

License

Copyright (c) 2022 European Journal of Pure and Applied Mathematics

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How to Cite

Restrained 2-Resolving Sets in the Join, Corona and Lexicographic Product of Two Graphs. (2022). European Journal of Pure and Applied Mathematics, 15(3), 1229-1236. https://doi.org/10.29020/nybg.ejpam.v15i3.4427