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arXiv · 1205.0102

The p-Domination Number of Complete Multipartite Graphs

You Lu·Jun-Ming Xu
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Abstract

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 $p$.

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You Lu, Jun-Ming Xu. 2012-05-01. The p-Domination Number of Complete Multipartite Graphs. https://arxiv.org/abs/1205.0102

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