Stable Locating-Dominating Sets in Graphs

  • 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
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

Published
2021-08-05
Section
Nonlinear Analysis