Stable Locating-Dominating Sets in Graphs

Eman Camad Ahmad, Gina Alquiza Malacas, Sergio Jr. Rosales Canoy

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.

Keywords

locating, stable, domination, join, corona

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