On Harmonic Index and Diameter of Unicyclic Graphs

被引：8

作者：

Jerline, J. Amalorpava ^{[1
]}

Michaelraj, L. Benedict ^{[2
]}

机构：

[1] Holy Cross Coll, Dept Math, Tiruchirappalli 620002, India

[2] St Josephs Coll, Dept Math, Tiruchirappalli 620002, India

来源：

IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS | 2016年 / 11卷 / 01期

关键词：

Harmonic index; Diameter; Unicyclic graph;

D O I：

10.7508/ijmsi.2016.01.010

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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 the vertex u in G. In this work, we prove the conjecture H(G)/D(G) >= 1/2 + 1/3(n - 1) given by Jianxi Liu in 2013 when G is a unicyclic graph and give a better bound H(G)/D(G) >= 1/2 + 2/3(n - 2), where m is the order and D(G) is the diameter of the graph G.

引用

页码：115 / 122

页数：8

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