论文标题
逆转图形中的单体动作和统治
Reversing monoid actions and domination in graphs
论文作者
论文摘要
给定图形$ g =（v，e）$，如果$ v \ backslash d $中的每个顶点在$ d $中相邻的每个顶点，则一组顶点$ d \ subseteq v $被称为主体集，而如果$ d $中的顶点与subset $ b \ subseteq v $相邻，则称为$ b \ subseteq v $，如果$ v-b $是$ v-b $，则称为nonblock v $。在本文中，我们介绍了一个图形动力学系统，该系统检测到通过反向系统的作用来统治和非封锁集的顶点集。此外，通过使用多个这样的图形动力学系统的动作，我们在两个字母上定义了自由单体的动作，反向动作中的元素对应于更特殊的主导集。
Given a graph $G=(V,E)$, a set of vertices $D\subseteq V $ is called a dominating set if every vertex in $V\backslash D$ is adjacent to a vertex in $D$, and a subset $B\subseteq V $ is called a nonblocking set if $V-B$ is a dominating set. In this paper, we introduce a graph dynamical systems detecting vertex sets that are simultaneously dominating and nonblocking sets via reversing the action of the system. Moreover, by using actions of multiple such graph dynamical systems we define actions of free monoid on two letters for which elements in the reverse action corresponds to more special dominating sets.
