Table of Contents
ISRN Combinatorics
Volume 2013 (2013), Article ID 906756, 5 pages
http://dx.doi.org/10.1155/2013/906756
Research Article

Wiener Index of Graphs with Radius Two

College of Mathematics and System Science, Xinjiang University, Urumqi, Xinjiang 830046, China

Received 20 December 2012; Accepted 21 January 2013

Academic Editors: J. Siemons and B. Taeri

Copyright © 2013 Yin Chen 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.

Abstract

The Wiener index of a graph is the sum of the distances between all pairs of vertices. It has been one of main descriptors that correlate a chemical compound's molecular graph with experimentally gathered data regarding the compound's characteristics. We characterize graphs with the maximum Wiener index among all graphs of order . with radius two. In addition, we pose a conjecture concerning the minimum Wiener index of graphs with given radius. If this conjecture is true, it will be able to answer an open question by You and Liu (2011).