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Journal of Applied Mathematics
Volume 2014, Article ID 316108, 9 pages
http://dx.doi.org/10.1155/2014/316108
Research Article

On Minimum Wiener Polarity Index of Unicyclic Graphs with Prescribed Maximum Degree

Department of Mathematics, Wuyi University, Jiangmen 529020, China

Received 6 April 2014; Accepted 15 July 2014; Published 9 November 2014

Academic Editor: Chongxin Liu

Copyright © 2014 Jianping Ou 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 polarity index of a connected graph is defined as the number of its pairs of vertices that are at distance three. By introducing some graph transformations, in different way with that of Huang et al., 2013, we determine the minimum Wiener polarity index of unicyclic graphs with any given maximum degree and girth, and characterize extremal graphs. These observations lead to the determination of the minimum Wiener polarity index of unicyclic graphs and the characterization of the extremal graphs.