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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 7241349, 5 pages
Research Article

The Hyper-Wiener Index of Trees of Order with Diameter

1School of Mathematics & Computation Sciences, Anqing Normal University, Anqing 246011, China
2Department of Mathematics, Southeast University, Nanjing, Jiangsu 210096, China
3Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia
4Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
5Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 23 March 2016; Accepted 31 August 2016

Academic Editor: Juan R. Torregrosa

Copyright © 2016 Gaixiang Cai et al. 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 hyper-Wiener index is a kind of extension of the Wiener index, used for predicting physicochemical properties of organic compounds. The hyper-Wiener index is defined as with the summation going over all pairs of vertices in , and denotes the distance of the two vertices and in the graph . In this paper, we obtain the second-minimum hyper-Wiener indices among all the trees with vertices and diameter and characterize the corresponding extremal graphs.