Mimus Edge Domination Numbers Of Graphs

The domination numbers of graphs play an important role in the structure of graphs.There are wide range of applications in coding theory,computer science, communication networks,surveillance systems,social networks,and other fields. Dunbar first introduced the signed domination number of graph.In 1998 Haynes published two monographs,in which a system overview of the domination theory is given,including signed domination number of graphs and minus domination number of graphs.These studies concentrate on vertices of graphs.Xu Bao-gen recently introduced edge domination numbers of graphs,and obtained some important results. Xu studied the minus edge domination numberr_m(G) of a graph and obtained two lower bounds of minus edge domination numbers,and determined minus edge domination numbers for complete graph,cycles and wheels.In this paper,we continue to investigate minus edge domination numbers.Local minus edge domination functions and local minus edge domination numbers of graphs are introduced in Chapter 2 to study minus edge domination numbers of graphs.The property of minimum local minus edge domination functions is given,the best bound of local minus edge domination numbers is obtained,local minus edge domination numbers of some special graphs are determined.Finally the upper bound of minus edge domination numbers of graphs is given.In Chapter 3 the best upper bound of minus edge domination number and two lower bound of minus edge domination numbers are given,minus edge domination numbers for some special graphs are determined.