三角格的拟完全控制
Quasiperfect domination in triangular lattices
摘要：
图$G$的顶点子集$S$是一个完美图（或称完美图）.若$G\setminus S$的每个顶点$v$只与$S$的一个顶点（$d_v\in\{1,2\}$顶点）相邻，则称$G$为$G$中的拟完全控制集.研究了Schläfli符号$\{3,6\}$的正则镶嵌图及其环面子图中的完全控制集和拟完全控制集，给出了它们的完全控制集和大多数具有$K_ν$形式导出分支的拟完全控制集$S$的分类，其中$ν\in\{1,2,3\}$仅依赖于$S$ .
英文摘要：
A vertex subset $S$ of a graph $G$ is a perfect (resp. quasiperfect) dominating set in $G$ if each vertex $v$ of $G\setminus S$ is adjacent to only one vertex ($d_v\in\{1,2\}$ vertices) of $S$. Perfect and quasiperfect dominating sets in the regular tessellation graph of Schläfli symbol $\{3,6\}$ and in its toroidal quotients are investigated, yielding the classification of their perfect dominating sets and most of their quasiperfect dominating sets $S$ with induced components of the form $K_ν$, where $ν\in\{1,2,3\}$ depends only on $S$.
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