We study upper bounds on the size of optimum locating-total dominating sets in graphs. A set $S$ of vertices of a graph $G$ is a locating-total dominating set if every vertex of $G$ has a neighbor in $S$, and if any two vertices outside $S$ have distinct neighborhoods within $S$. The smallest size of such a set is denoted by $\gamma^L_t(G)$. It has been conjectured that $\gamma^L_t(G)\leq\frac{2n}{3}$ holds for every twin-free graph $G$ of order $n$ without isolated vertices. We prove that the conjecture holds for cobipartite graphs, split graphs, block graphs and subcubic graphs.

翻译：我们研究了图中最优定位全控制集大小的上界。图$G$的顶点集$S$若满足：$G$的每个顶点在$S$中至少有一个邻点，且$S$外任意两个顶点在$S$内的邻域互不相同，则称$S$为定位全控制集。该集的最小规模记为$\gamma^L_t(G)$。已有猜想指出：对于任意$n$阶无孤立顶点的无孪生顶点图$G$，均有$\gamma^L_t(G)\leq\frac{2n}{3}$。本文证明了该猜想在共二部图、分裂图、块图和次立方图中均成立。