A characterization of locating-domination edge critical graphs.
Mostafa Blidia, Widad Dali · 2009
A locating-dominating set D of a graph G =(V (G),E(G)) is a set D ⊆ V (G) such that every vertex of V (G) − D is adjacent to a vertex of D and for every pair of distinct vertices u, v in V (G) − D, N(u) ∩ D = N(v) ∩ D. The minimum cardinality of a locating-dominating set is denoted by γL(G). A graph G is said to be a locating domination edge removal critical graph, orjustγ + L-ER-critical graph, if γL(G−e)>γL(G) for all e ∈ E(G). The purpose of this paper is to characterize the class of-ER-critical graphs. γ + L 1