Locating-total domination in claw-free cubic graphs

In this paper, we continue the study of locating-total domination in graphs. A set S of vertices of a graph G is a total dominating set of G if every vertex of G is adjacent to a vertex in S . We consider total dominating sets S which have the additional property that distinct vertices in V ( G ) ∖ S are totally dominated by distinct subsets of the total dominating set. Such a set S is called a locating-total dominating set in G , and the locating-total domination number of G is the minimum cardinality of a locating-total dominating set in G . A claw-free graph is a graph that does not contain K 1 , 3 as an induced subgraph. We show that the locating-total domination number of a claw-free cubic graph is at most one-half its order and we characterize the graphs achieving this bound.