A note on -vertex critical graphs

Abstract

A locating-total dominating set of a graph G = (V(G), E(G)) with no isolated vertex is a set S ⊆ V(G) such that every vertex of V(G) is adjacent to a vertex of S and for every pair of distinct vertices u and v in V(G) − S, N(u) ∩ S = N(v) ∩ S. Let be the minimum cardinality of a locating-total dominating set of G. A graph G is said to be locating-total domination vertex critical if for every vertex w, G − w has no isolated vertex and . In this note, we characterize locating-total domination vertex critical Unicycle graphs.