Harmonic index of dense graphs

被引：0

作者：

Liu, Jianxi ^{[1
]}

机构：

[1] Guangdong Univ Foreign Studies, Sch Informat, Dept Appl Math, Guangzhou 510006, Guangdong, Peoples R China

来源：

ARS COMBINATORIA | 2015年 / 120卷

基金：

中国国家自然科学基金;

关键词：

Harmonic index; dense graphs; minimum value; SUM-CONNECTIVITY INDEX; CONJECTURE; AOUCHICHE; HANSEN;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The harmonic weight of an edge is defined as reciprocal of the average degree of its end-Vertices. The harmonic index of a graph G is defined as the sum of all harmonic weights of its edges. In this work, we give the minimum value of the harmonic index for any n-vertex connected graphs with minimum degree 5 at least k(>= n/2) and show the corresponding extremal graphs have only two degrees, i.e., degree k and degree n - 1, and the number of vertices of degree k is as close to n/2 as possible.

引用

页码：293 / 304

页数：12

共 27 条

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