Stable Locating-Dominating Sets in Graphs

Authors

  • Eman Camad Ahmad Mindanao State University-Iligan Institute of Technology
  • Gina Alquiza Malacas Mindanao State University-Iligan Institute of Technology
  • Sergio Jr. Rosales Canoy Mindanao State University-Iligan Institute of Technology

DOI:

https://doi.org/10.29020/nybg.ejpam.v14i3.3998

Keywords:

locating, stable, domination, join, corona

Abstract

A set S ⊆ V(G) of a (simple) undirected graph G is a locating-dominating set of G if for each v ∈ V(G) \ S, there exists w ∈ S such tha vw ∈ E(G) and NG(x) ∩ S= NG(y)∩S for any distinct vertices x and y in V(G) \ S. S is a stable locating-dominating set of G if it is a locating-dominating set of G and S \ {v} is a locating-dominating set of G for each v ∈ S. The minimum cardinality of a stable locating-dominating set of G, denoted by γsl(G), is called the stable locating-domination number of G. In this paper, we investigate this concept and the corresponding parameter for some graphs. Further, we introduce other related concepts and use them to characterize the stable locating-dominating sets in some graphs.

Author Biographies

  • Eman Camad Ahmad, Mindanao State University-Iligan Institute of Technology
    Department of Mathematics and Statistics
  • Gina Alquiza Malacas, Mindanao State University-Iligan Institute of Technology

    Professor

    Department of Mathematics and Statistics

  • Sergio Jr. Rosales Canoy, Mindanao State University-Iligan Institute of Technology

    Professor

    Department of Mathematics and Statistics

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Published

2021-08-05

Issue

Vol. 14 No. 3: (July 2021)

Section

Nonlinear Analysis

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How to Cite

Stable Locating-Dominating Sets in Graphs. (2021). European Journal of Pure and Applied Mathematics, 14(3), 638-649. https://doi.org/10.29020/nybg.ejpam.v14i3.3998