A lower bound for the harmonic index of a graph with minimum degree at least two

被引：61
|
作者：
Wu, Renfang [1 ]
Tang, Zikai [1 ]
Deng, Hanyuan [1 ]
机构：
[1] Hunan Normal Univ, Minist Educ China, Coll Math & Comp Sci, Key Lab High Performance Comp & Stochast Informat, Changsha 410081, Hunan, Peoples R China
来源：
FILOMAT | 2013年 / 27卷 / 01期
关键词：
Graph; the harmonic index; the minimum degree;
D O I：
10.2298/FIL1301051W
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The harmonic index H(G) of a graph G is defined as the sum of the weights 2/ d(u)+ d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. We give a best possible lower bound for the harmonic index of a graph (a triangle-free graph, respectively) with minimum degree at least two and characterize the extremal graphs.
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页码：51 / 55
页数：5
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