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2014•Discrete Mathematics Algorithms and ApplicationsRequires access

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 be a positive integer. A subset S ⊆ 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. This paper establishes an exact formula of the p-domination number of all complete multipartite graphs for arbitrary positive integer p.

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What this paper is about

Let G = (V, E) be a graph and p be a positive integer. A subset S ⊆ 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. This paper establishes an exact formula of the p-domination number of all complete multipartite graphs for arbitrary positive integer p.

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Available abstract

Let G = (V, E) be a graph and p be a positive integer. A subset S ⊆ 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. This paper establishes an exact formula of the p-domination number of all complete multipartite graphs for arbitrary positive integer p.

Key concepts: Multipartite, Dominating set, Combinatorics, Mathematics, Domination analysis, Vertex (graph theory), Discrete mathematics, Graph

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