Geodesic
An upper bound for domination number of 5-regular graphs
Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 1049-1061

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Let $G=(V, E)$ be a simple graph. A subset $S\subseteq V$ is a dominating set of $G$, if for any vertex $u\in V-S$, there exists a vertex $v\in S$ such that $uv\in E$. The domination number, denoted by $\gamma (G)$, is the minimum cardinality of a dominating set. In this paper we will prove that if $G$ is a 5-regular graph, then $\gamma (G)\le {5\over 14}n$.
Classification : 05C69
Keywords: domination number; 5-regular graph; upper bounds 
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     title = {An upper bound for domination number of 5-regular graphs},
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Xing, Hua-Ming; Sun, Liang; Chen, Xue-Gang. An upper bound for domination number of 5-regular graphs. Czechoslovak Mathematical Journal, Tome 56 (2006) no. 3, pp. 1049-1061. http://geodesic.mathdoc.fr/item/CMJ_2006__56_3_a22/