Locating-total domination in claw-free cubic graphs

In this paper, we continue the study of locating-total domination in graphs. A set SS of vertices of a graph GG is a total dominating set of GG if every vertex of GG is adjacent to a vertex in SS. We consider total dominating sets SS which have the additional property that distinct vertices in V(G)∖SV(G)∖S are totally dominated by distinct subsets of the total dominating set. Such a set SS is called a locating-total dominating set in GG, and the locating-total domination number of GG is the minimum cardinality of a locating-total dominating set in GG. A claw-free graph is a graph that does not contain K1,3K1,3 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.