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An upper bound for domination number of 5-regular graphs

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Abstract

Let G = (V, E) be a simple graph. A subset S ⊆ V is a dominating set of G, if for any vertex u ∈ V-S, there exists a vertex v ∈ S such that uv ∈ E. The domination number, denoted by γ(G), is the minimum cardinality of a dominating set. In this paper we will prove that if G is a 5-regular graph, then γ(G) ⩽ 5/14n.

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Authors and Affiliations

  1. Dept. of Mathematics, Langfang Teachers College, Langfang, Hebei, 065000, P. R. China

    Hua-Ming Xing

  2. Dept. of Mathematics, Beijing Institute of Technology, Beijing, 100081, P. R. China

    Liang Sun

  3. College of Info. Sci. & Eng., Shandong University of Sci. & Tech., Taian, 271019, P. R. China

    Xue-Gang Chen

Authors
  1. Hua-Ming Xing
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  2. Liang Sun
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  3. Xue-Gang Chen
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Xing, HM., Sun, L. & Chen, XG. An upper bound for domination number of 5-regular graphs. Czech Math J 56, 1049–1061 (2006). https://doi.org/10.1007/s10587-006-0079-4

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  • DOI: https://doi.org/10.1007/s10587-006-0079-4

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