SHANDONG SCIENCE ›› 2016, Vol. 29 ›› Issue (1): 83-86.doi: 10.3976/j.issn.1002-4026.2016.01.014

• Other Research Article • Previous Articles     Next Articles

Harmonic index of tree and unicyclic graphs

Wang Xiao   

  1. School of Mathematics and Computer Engineering, Shangluo University, Shangluo 726000, China
  • Received:2015-04-23 Published:2016-02-20 Online:2016-02-20

Abstract:

We obtain two lemmas for harmonic index of graphs through the transforms changing leaf numbers.We further prove the sharp bounds for harmonic index of tree and unicyclic graphs with fixed order.We also present the corresponding extremal graphs.

Key words: tree graphs, harmonic index, unicyclic graphs

CLC Number: 

  • O157.5

Open Access This article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), which permits third parties to freely share (i.e., copy and redistribute the material in any medium or format) and adapt (i.e., remix, transform, or build upon the material) the articles published in this journal, provided that appropriate credit is given, a link to the license is provided, and any changes made are indicated. The material may not be used for commercial purposes. For details of the CC BY-NC 4.0 license, please visit: https://creativecommons.org/licenses/by-nc/4.0