(untitled) (European Journal of Pure and Applied Mathematics, 2023)
A set S ⊆ V (G) of an 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 two 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 γSLD(G), is called the stable locating-domination number of G. In this paper, we investigate this concept and the corresponding parameter for edge corona and lexicographic product of graphs.