The connectivity and the Harary index of a graph

被引：30
作者：
Li, Xiao-Xin [1 ,2 ]
Fan, Yi-Zheng [2 ]
机构：
[1] Chizhou Univ, Dept Math, Chizhou 247000, Peoples R China
[2] Anhui Univ, Sch Math Sci, Hefei 230601, Peoples R China
来源：
DISCRETE APPLIED MATHEMATICS | 2015年 / 181卷
基金：
中国国家自然科学基金;
关键词：
Graph; Harary index; Cut vertex; Vertex connectivity; Edge connectivity; HYPER-WIENER; MATRIX;
D O I：
10.1016/j.dam.2014.08.022
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Harary index of a graph is defined as the sum of reciprocals of distances between all pairs of vertices of the graph. In this paper we provide an upper bound of the Harary index in terms of the vertex or edge connectivity of a graph. We characterize the unique graph with the maximum Harary index among all graphs with a given number of cut vertices or vertex connectivity or edge connectivity. In addition we also characterize the extremal graphs with the second maximum Harary index among all graphs with given vertex connectivity. (C) 2014 Elsevier B.V. All rights reserved.
引用
收藏
页码：167 / 173
页数：7
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