有关完全图的图的紧性  

The Compactness of Graph About Complete Graphs

作　　者：斯琴巴特尔[1] 王井玉[1] 

机构地区：[1]内蒙古民族大学数学学院,内蒙古通辽028043

出　　处：《数学的实践与认识》2016年第18期229-234,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(No61262018)

摘　　要：双随机矩阵有许多重要的应用,紧图族可以看作是组合矩阵论中关于双随机矩阵的著名的Birkhoff定理的拓广,具有重要的研究价值.确定一个图是否紧图是个困难的问题,目前已知的紧图族尚且不多,给出了三个结果:任意多个完全图的不交并是紧图;圈C_3与圈C_n(n>3)的不交并是非紧图;当n是大于等于3的奇数时,完全图K_n与图K_(n+1)的不交并是非紧图,其中图K_(n+1)是从完全图K_(n+1)删去一因子而得到的图.Doubly stochastic matrix has many important applications,the family of compact graphs can be seen as the generaUzation of the famous Birkhoff theorem which is about doubly stochastic matrix,and is of important research value.Determine whether a graph is a compact graph is a difficult problem,at present there are only few compact graphs known.This paper gives three important results：the disjoint union of any number of the complete graphs is compact graph;the disjoint union of circle C_3 and circle C_n（n 3） is non- compact graph;when n is an odd number and equal or greater than 3,the disjoint union of the complete graph K_n and the graph K_（n＋1） is non- compact graph,where the graph K_（n＋1） is obtained by deleting 1- factor from the complete graph K_（n＋1）

关 键 词：完全图 不交并 紧图 非紧图 

分 类 号：O157.5[理学—数学]