连通图的Harary指数上界及其极图  

An upper bound for the Harary index of a connected graph and the corresponding extremal graph

作　　者：李小新[1] 查淑萍[2] 范益政[3] 

机构地区：[1]池州学院数学系,安徽池州247000 [2]安庆师范学院数学与计算科学学院,安徽安庆246133 [3]安徽大学数学科学学院,安徽合肥230601

出　　处：《中国科学技术大学学报》2014年第2期96-100,共5页JUSTC

基　　金：国家自然科学基金(11071002);安徽省教育厅自然科学研究重点项目(KJ2013A196)资助

摘　　要：图的Harary指数定义为图的所有顶点对的距离的倒数之和.刻画了在给定点数和直径的图类中,Harary指数达到最大的极图,并由此确定了Harary指数关于直径的一个上界.另外,在n阶连通图中,刻画了Harary指数达到第二大和第三大的图的结构.The Harary index of a graph is defined as the sum of reciprocals of distances between all pairs of vertices of the graph. The graph（s） with maximum Harary index among all graphs with given order and diameter was characterized, and an upper bound for the Harary index in terms of diameter was provided. In addition, the connected graphs of order n with the second maximum and the third maximum Harary indices were characterized, respectively.

关 键 词：图 Harary指数 直径 

分 类 号：O157.5[理学—数学]