Major Independence Number In Graphs

In this paper,we discuss concepts of some independence number in graphs and study nature characteristics of some independence number in graphs,then we put focus on three problems,as follows,signed independence number in graphs,major independence number in graphs,k signed independence number in graphs.The graph connectivity is a key parameter to measure the graph connectivity.In this paper,we solve signed independence number of connected graphs with order n,the minimum degree ? and signed independence number's upper bounds of connected graphs with order n,besides we discuss the relation between signed independence number in graphs and signed domination number in graphs.In this paper,we introduce a concept of major independence number in graphs and study nature characteristics of major independence number in graphs,We mainly establish major independence number's upper bounds of connected graphs with order n and major independence numbers of some special graphs,for example complete graphs,complete bipartite graphs,stars,a path,a circle and so on.Then we discuss major independence number's bounds of some graphs,and we discuss the minimum order of a connected graph with the major independence number that is given and major independence number'maximum of graphs with order n,the givien degree.At last,we introduce a concept of maximum major independence function in graphs and study nature characteristics of maximum major independence function in graphs in this paper.At last we introduce a concept of k signed independence number in graphs and study nature characteristics of maximum major independence number in graphs in this paper,respectively k signed independence number's upper bounds of graphs with order n,the degree sequence that is givien,k signed independence number's upper bounds of r regular graphs with order n,k signed independence number's upper bounds of graphs with order n,edge m and maximum degree that is givien.