  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 $p$.
