On connected 3-γL-dot-critical graphs

A set D of vertices in a graph G is a locating-dominating set if for every two vertices u,v of V-D the sets N(u)∩D and N(v)∩D are non-empty and different. The locating-domination number γ L (G) is the minimum cardinality of a locating-dominating set of G. A graph G is γ L -dot-critical if contracting any edge of G decreases its locating-domination number. Let k≥3 be an integer. A graph G is called k-γ L -dot-critical if G is γ L -dot-critical with γ L (G)=k. In this paper, we characterize all connected 3-γ L -dot-critical graphs.