Locating-total domination in graphs

In this paper, we continue the study of locating-total domination in graphs. A set S of vertices in a graph G is a total dominating set in 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. We obtain new lower and upper bounds on the locating-total domination number of a graph. Interpolation results are established, and the locating-total domination number in special families of graphs, including cubic graphs and grid graphs, is investigated.