标题： p-支配数的完全多部图 显示英文标题

标题： The p-Domination Number of Complete Multipartite Graphs

摘要： 设 $G=(V,E)$ 是一个图， $p$ 是一个正整数。 一个子集$S\subseteq V$被称为图$G$的$p$-支配集，如果不在$S$中的每个顶点在$S$中至少有$p$个邻接点。 The $p$-domination number is the minimum cardinality of a $p$-dominating set in $G$. In this paper, we establish an exact formula of the $p$-domination number of all complete multipartite graphs for arbitrary positive integer $p$. 显示英文摘要

摘要： Let $G=(V,E)$ be a graph and $p$ a positive integer. A subset $S\subseteq V$ is called a $p$-dominating set of $G$ if every vertex not in $S$ has at least $p$ neighbors in $S$. The $p$-domination number is the minimum cardinality of a $p$-dominating set in $G$. In this paper, we establish an exact formula of the $p$-domination number of all complete multipartite graphs for arbitrary positive integer $p$.