| Let G=(V,E)be a simple graph.D?V(G),for any v∈V(G),there exists a vertex u∈D,such that d(u,v)≤r,then D is said to be a r-distance domination set.If D is r-distance domination set of G,and for any two different vertices u,v∈V(G)\D,we have Dr(v)≠Dr(u)≠?,D is called a r-distance locating dominating set(r-LDS).Q ? V(G),for a vertex v ∈ V(G)\Q in the graph G,there are at least two vertices adjacent to v in Q,then Q is said to be a 2-domination set of G.An independent set of a graph G is a set consisting of two non-adjacent vertices.If J is a 2-domination set and an independent set,then J is a 2-independent domination set of the graph G.A function f:V→{-1,1} is a signed dominating function if for any vertex v∈v,f(N[v])≥ 1.The weight of function f is ∑v∈V f(V).The signed dominating number of a graph G is defined as γs(G)=min{f(V)|f is the signed dominating function of graph G}.In this thesis,based on the concept of product graph and domination parameters,we study three domination parameters of three product graphs of several kinds of graphs.Firstly,according to the 1-distance locating dominating of paths and cycles,study the 1-distance locating dominating of their Corona product,get the optimal 1-distance locating dominating set,and give the 1-distance locating dominating upper bound of the Cartesian product graph,also get the result about the 1-distance locating dominating set on the direct product according to the property of direct product.Then,based on the study of independent domination numbers on various types of graphs,the 2-independent domination sets of the graph Corona product,Cartesian product graphs,and the direct product are computed.Finally,we give the signed dominating numbers or bounds for the Corona product,Cartesian product graphs,and the direct product. |
