EDS指数与平衡二部图的哈密尔顿性  

EDS Index and Hamiltonicity of Balanced Bipartite Graph

作　　者：李青 刘莉 袁慧 LI Qing;LIU Li;YUAN Hui(Department of Public Teaching,Hefei Preschool Education College,Hefei 230013,China;School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]合肥幼儿师范高等专科学校公共教学部,安徽合肥230013 [2]安庆师范大学数理学院,安徽安庆246133

出　　处：《长春师范大学学报》2023年第6期6-10,46,共6页Journal of Changchun Normal University

基　　金：安徽省自然科学基金项目“图的哈密尔顿性的谱与拓扑指数的刻画”(1808085MA04);安徽高校自然科学研究重点项目“关于谱与拓扑指数极图的研究”(KJ2020A0894);合肥幼儿师范高等专科学校教科研重点项目“图的拓扑指数与哈密尔顿性”(hykyzd202206)。

摘　　要：如果一个图的顶点集可以划分为两个不相交的子集X和Y,这里|X|=|Y|,使得每条边都有一个端点在X中,另一个端点在Y中,那么称此图为平衡二部图.本文利用平衡二部图的特殊结构找到了原图或其拟补图关于EDS指数的界,结合平衡二部图中特殊性质的度序列与边条件,根据原图或其拟补图的EDS指数分别给出一个平衡二部图是可迹的、哈密尔顿或弱哈密尔顿-连通的充分条件.A graph is balanced bipartite graph if its set can be divided into two non-intersecting subsets X and Y,where |X|=|Y|,so that every edge has one end in X and the other end in Y.In this paper,we use the special structure of the balanced bipartite graph to find the bounds of EDS index in the original graph or the quasi-complement graph.Then we combine the special degree sequence and the edge condition in the balanced bipartite graph.Finally,the sufficient conditions for a balanced bipartite graph to be traceable,Hamiltonian or weakly Hamilton-connected are given according to the EDS index of the original graph or the quasi-complement of the graph respectively.

关 键 词：平衡二部图 拟补图 哈密尔顿性 EDS指数 

分 类 号：O157.5[理学—数学]