(1) Department of Applied Mathematics, Beijing Institute of Technology, Beijing, 100081, P. R. China;(2) Department of Applied Mathematics, Beijing Institute of Technology, Beijing, 100081, P.R. China
Abstract:
Let G be a simple graph. A subset SV is a dominating set of G, if for any vertex vV – S there exists a vertex uS such that uvE(G). The domination number, denoted by (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 (G) 4/11n
V is a dominating set of G, if for any vertex v 
V – S there exists a vertex u 
(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 
4/11 n