The Relationship Between Various Nomination Parameteres Of Graph

On the relationship between sum domination parameteres of graphs,domination parameteres have been studied extensively because of wide applications in the fields of computer science and network communication.Research on domination parameters thoery mainly concentrate on the following aspects:(l)Discussing the relationships between various domination parameters;(2)Establishing the bounds on various domination parameteres and the relationships between domination parameteres involving other graph indexes;(3)Constructing algorithm of domination parameteres and discussing computation complexitis.It is divided into the following parts:Chapter 1 Intoduction.Chapter2 The concepts of graphs and domination parameters and some functions.Chapter3 The concepts of k-domination parameters and some important thoertis.Maily proving the inequality for k-connected domination number:For G is connected,then we haveγ_k~c (G)≤(2k +(?))ir_k (G) - 2k,γ_k~c (G), ir_k (G) denote the k-connected domination number and k-irredundancenumber.When k=l,the result become another result in[25].Chapter4 Discussing the Nordhaus-Gaddum results for several domination-related parameters.Letλ(G) be a parameter for a graph G, the Nordhaus-Gaddum result is defined the inequalities for the sum and multiplication ofλ(G) andλ((?)) .In this note we prove a conjecture due to Haray and Haneys[32] saying that if a graph hasγ(G)≥4,γ((?))≥4 ,thenandWhereγ_p (G) andγ_t(G) denote pair domination number and total domination number.Whenγ(G) =γ((?)) = 4 ,it become the conjecture in[32].