Signed Star Independent Number Of Graphs

This paper mainly studies the signed star independent number and the signed star kindependent number of graphs,focusing on two problems: the signed star independent number and k-independent number of graphs,the signed star independent number and the signed star k-independent number of the special graphs.The control theory of graph is an important research branch of graphs theory.In recent years,the control theory of the graphs has gradually developed from the traditional point control number to the edge control number,and the proposal and research of various border control numbers have greatly enriched and developed the control theory of the graphs.Among them,the signed star control number of the graphs is an important edge control number.In this paper,the concept of signed star control number of the graph,introduce the concept of the signed star independent number of the graph,give the signed star independent number of the graph and some related concepts,and on this basis,the natural promotion,thus introducing the signed star k-independent function of the graph and the concept of the signed star kindependent number of the graph.This paper mainly studies the signed star independent number and some special graph of the signed star independent number and the signed star k-independent number.The study of the signed star independent number of the graph: First,the definition of the signed star independent number and related concepts of the graph is given,including the concept of the signed star independent function of the graph,the signed star independent number of the graph,the signed star independent edge set of the graph,and so on;Including the upper bound of the general graph signed star independent number(in fact,the upper bound is the best possible),as well as the tree diagram,two graph,the interconnect graph of the signed star independent number of the lower bounds,further,give the forest and the general graph of the signed star independent number of the lower bounds;The number of signed stars independent of a full two-part diagram.The study of the symbol star k-independent number of the graph: First,the definition of the symbol star k-independent number and related concepts of the graph is given,and some examples related to it,and then,the two upper bounds of the symbol star kindependent number of the graph are given.Finally,the symbol star k-independent number of the special graph is introduced,including the symbol star k-independent number of Road P_n and Circle C_n.