Minimum harmonic indices of trees and unicyclic graphs with given number of pendant vertices and diameter

被引：0

作者：

Zhu, Yan ^{[1
]}

Chang, Renying ^{[2
]}

机构：

[1] E China Univ Sci & Technol, Dept Math, Shanghai 200237, Peoples R China

[2] Linyi Univ, Dept Math, Linyi 276005, Shandong, Peoples R China

来源：

UTILITAS MATHEMATICA | 2014年 / 93卷

关键词：

Harmonic index; tree; unicyclic graph; pendant vertice; diameter;

D O I：

暂无

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 weights 2/d(u)+d(v) of all edges uv of G, where d(u) denotes the degree of a vertex u in G. In this paper, we give sharp lower bounds for harmonic indices of trees and unicyclic graphs with n vertices and k pendant vertices, and characterize the corresponding extremal graphs. Furthermore, we also determine the smallest harmonic index of trees and unicyclic graphs with n vertices and diameter D(G).

引用

页码：365 / 374

页数：10

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