The p-Domination Number of Complete Multipartite Graphs

TL;DR

This paper derives an exact formula for the p-domination number of complete multipartite graphs, extending understanding of domination parameters in graph theory.

Contribution

It provides a precise formula for the p-domination number in all complete multipartite graphs, a significant extension in domination theory.

Findings

Exact formula for p-domination number in complete multipartite graphs

Generalizes previous results for specific cases

Enhances understanding of domination parameters in graph theory

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 $p$.