Table of Contents
ISRN Applied Mathematics
Volume 2014, Article ID 781648, 8 pages
Research Article

Some Properties on the Harmonic Index of Molecular Trees

School of Mathematics and Statistics, Minnan Normal University, Zhangzhou, Fujian 363000, China

Received 4 October 2013; Accepted 4 December 2013; Published 29 January 2014

Academic Editors: A. J. Kearsley and X. Liu

Copyright © 2014 Shaoqiang Liu and Jianxi Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The harmonic index of a graph is defined as the sum of weights of all edges of , where denotes the degree of the vertex in . In this paper, some general properties of the harmonic index for molecular trees are explored. Moreover, the smallest and largest values of harmonic index for molecular trees with given pendent vertices are provided, respectively.