On domination number of 4-regular graphs

Liu, Hailong, and Sun, Liang. "On domination number of 4-regular graphs." Czechoslovak Mathematical Journal 54.4 (2004): 889-898. <http://eudml.org/doc/30908>.

@article{Liu2004,
abstract = {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 $\gamma (G) \le \frac\{4\}\{11\}n$.},
author = {Liu, Hailong, Sun, Liang},
journal = {Czechoslovak Mathematical Journal},
keywords = {regular graph; dominating set; domination number; regular graph; dominating set; domination number},
language = {eng},
number = {4},
pages = {889-898},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On domination number of 4-regular graphs},
url = {http://eudml.org/doc/30908},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Liu, Hailong
AU - Sun, Liang
TI - On domination number of 4-regular graphs
JO - Czechoslovak Mathematical Journal
PY - 2004
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 54
IS - 4
SP - 889
EP - 898
AB - 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 $\gamma (G) \le \frac{4}{11}n$.
LA - eng
KW - regular graph; dominating set; domination number; regular graph; dominating set; domination number
UR - http://eudml.org/doc/30908
ER -