On Domination Number of 4-Regular Graphs

@article{Liu2004OnDN,
  title={On Domination Number of 4-Regular Graphs},
  author={Hailong Liu and Liang Sun},
  journal={Czechoslovak Mathematical Journal},
  year={2004},
  volume={54},
  pages={889-898}
}
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) ≤ 4/11n 

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