论文标题
平面三角形的总统治
Total domination in plane triangulations
论文作者
论文摘要
图$ g =（v，e）$的总占主导地位是$ v $的子集$ d $ d $，因此$ v $中的每个顶点都与$ d $中的至少一个顶点相邻。 $ g $的总统统治数是$γ_T（g）$表示的，是$ g $的总统治组的最低基数。几乎三角形的是双连接的平面图，该图的平面图承认了一个嵌入的平面，使其所有的脸都是三角形的，除了外脸外。我们在本文中表明$γ_t（g）\ le \ lfloor \ frac {2n} {5} {5} \ rfloor $对于任何接近三角形的$ g $ of订单$ n \ ge 5 $，有两个例外。
A total dominating set of a graph $G=(V,E)$ is a subset $D$ of $V$ such that every vertex in $V$ is adjacent to at least one vertex in $D$. The total domination number of $G$, denoted by $γ_t (G)$, is the minimum cardinality of a total dominating set of $G$. A near-triangulation is a biconnected planar graph that admits a plane embedding such that all of its faces are triangles except possibly the outer face. We show in this paper that $γ_t (G) \le \lfloor \frac{2n}{5}\rfloor$ for any near-triangulation $G$ of order $n\ge 5$, with two exceptions.
