文献类型：期刊文献

英文题名：Minimum harmonic indices of trees and unicyclic graphs with given number of pendant vertices and diameter

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

年份：2014

卷号：93

起止页码：365

外文期刊名：UTILITAS MATHEMATICA

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000332188500032)】；

基金：This research was supported by the Fundamental Research Funds for the Central Universities, SRFDP(20130074120021) and SRF for ROCS, SEM.

语种：英文

外文关键词：Harmonic index; tree; unicyclic graph; pendant vertice; diameter

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).