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On Domination Number of 4-Regular Graphs

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Abstract

Let G be a simple graph. A subset S ⫅ V is a dominating set of G, if for any vertex v ∈ V – S there exists a vertex u ∈ S such that uv ∈ E(G). The domination number, denoted by γ(G), is the minimum cardinality of a dominating set. In this paper we prove that if G is a 4-regular graph with order n, then γ(G) ≤ 4/11 n

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Authors and Affiliations

  1. Department of Applied Mathematics, Beijing Institute of Technology, Beijing, 100081, P. R. China

    Hailong Liu

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

    Liang Sun

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  1. Hailong Liu
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  2. Liang Sun
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Correspondence to Hailong Liu or Liang Sun.

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Liu, H., Sun, L. On Domination Number of 4-Regular Graphs. Czech Math J 54, 889–898 (2004). https://doi.org/10.1007/s10587-004-6438-0

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  • DOI: https://doi.org/10.1007/s10587-004-6438-0

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