论文标题
朝着定位统计支配集的三分之二猜想的进展
Progress towards the two-thirds conjecture on locating-total dominating sets
论文作者
论文摘要
我们研究了图中最佳定位统计支配集的大小。如果每个顶点的$ g $在$ s $中都有一个邻居，并且如果$ s $中的每个顶点都有一个邻居，并且如果$ s $以外的$ s $以外的任何两个顶点在$ s $中都有不同的社区，则图形$ g $的$ s $是定位的主导套装。 $γ^l_t（g）$表示这种集合的最小尺寸。据推测，每一个无隔离顶点的$γ^l_t（g）\ leq \ frac {2n} {3} $保留的每二个$ g $ g $ g $ g $ g $ of drops $ n $。我们证明该猜想适用于鹅卵石图，拆分图，块图和亚立管图。
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 $γ^L_t(G)$. It has been conjectured that $γ^L_t(G)\leq\frac{2n}{3}$ 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.
