On The Edge-balance Index Sets Of Chain Sums Of K_4-e

Boolean index set of graph is an important part of Graph theory, Boolean index settheory can be applied to information engineering, communication networks,computerscience,economic management,medicine, etc. The edge-balance index set is an im-portant issue in Boolean index set, in this paper, we will study the edge-balance indexsets of K4 - e .In chapter 1, some conclusions about Boolean index sets of graphs are introduced,and Some prior knowledge are provided.In chapter 2, we study the edge-balance index sets of the ?rst type of chain-sumsof K4 - e by the graphical construction method and analysis of induction .In chapter 3, the perfect index set and the complete index set of the ?rst type ofchain-sums of K4 - e are de?ned, and necessary and su?cient condition that B(n)(n isodd) exist the perfect index set and the complete index set , are given.In chapter 4, using methods similar to those of Chapter 2, the edge-balance indexsets of the second type of chain-sums of K4-e, are researched, and graphical constructionmethod of the corresponding graph is given.Finally, we identify the edge-balance index sets of chain sums of K4 -e completely,and solve the graphical construction method of each category index about the edge-balance index set.