An upper bound for domination number of 5-regular graphs |
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| Authors: | Hua-Ming Xing Liang Sun Xue-Gang Chen |
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| Institution: | (1) Dept. of Mathematics, Langfang Teachers College, Langfang, Hebei, 065000, P. R. China;(2) Dept. of Mathematics, Beijing Institute of Technology, Beijing, 100081, P. R. China;(3) College of Info. Sci. & Eng., Shandong University of Sci. & Tech., Taian, 271019, P. R. China |
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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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| Keywords: | domination number 5-regular graph upper bounds |
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