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

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How to Cite

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