On Domination Number of 4-Regular Graphs
Hailong Liu, Liang Sun · Czechoslovak Mathematical Journal · 2004
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