On Movable Strong Resolving Domination in Graphs

Authors

  • Helyn Cosinas Sumaoy Mindanao State University - Iligan Institute of Technology
  • Helen Rara Center of Graph Theory, Algebra and Analysis - Premier Research Institute of Science and Mathematics Mindanao State University - Iligan Institute of Technology College of Science and Mathematics

DOI:

https://doi.org/10.29020/nybg.ejpam.v15i3.4440

Keywords:

Movable strong resolving dominating set, movable strong resolving domination number, lexicographic product

Abstract

Let G be a connected graph. A strong resolving dominating set S is a 1-movable strong resolving dominating set of G if for every v ∈ S, either S \ {v} is a strong resolving dominating set or there exists a vertex u ∈ (V (G) \ S) ∩ NG(v) such that (S \ {v}) ∪ {u} is a strong resolving dominating set of G. The minimum cardinality of a 1-movable strong resolving dominating set of G,
denoted by γ1 msR(G) is the 1-movable strong resolving domination number of G. A 1-movable strong resolving dominating set with cardinality γ1msR(G) is called a γ1msR-set of G. In this paper, we study this concept and the corresponding parameter in graphs resulting from the join, corona and lexicographic product of two graphs. Specifically, we characterize the 1-movable strong resolving
dominating sets in these types of graphs and determine the exact values of their 1-movable strong resolving domination numbers.

Author Biography

  • Helen Rara, Center of Graph Theory, Algebra and Analysis - Premier Research Institute of Science and Mathematics Mindanao State University - Iligan Institute of Technology College of Science and Mathematics

    Department of Mathematics and Statistics

    Professor VI

Downloads

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

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

On Movable Strong Resolving Domination in Graphs. (2022). European Journal of Pure and Applied Mathematics, 15(3), 1201-1210. https://doi.org/10.29020/nybg.ejpam.v15i3.4440