Geodesic
On domination number of 4-regular graphs
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 4, pp. 889-898
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Let $G$ be a simple graph. A subset $S \subseteq V$ is a dominating set of $G$, if for any vertex $v \in V~- S$ there exists a vertex $u \in S$ such that $uv \in E (G)$. The domination number, denoted by $\gamma (G)$, 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 $\gamma (G) \le \frac{4}{11}n$.
Let $G$ be a simple graph. A subset $S \subseteq V$ is a dominating set of $G$, if for any vertex $v \in V~- S$ there exists a vertex $u \in S$ such that $uv \in E (G)$. The domination number, denoted by $\gamma (G)$, 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 $\gamma (G) \le \frac{4}{11}n$.
Classification : 05C69
Keywords: regular graph; dominating set; domination number 
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Liu, Hailong; Sun, Liang. On domination number of 4-regular graphs. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 4, pp. 889-898. http://geodesic.mathdoc.fr/item/CMJ_2004_54_4_a5/

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