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Journal of Chemistry
Volume 2014, Article ID 742121, 4 pages
http://dx.doi.org/10.1155/2014/742121
Research Article

The Wiener Index of Circulant Graphs

Department of Mathematics, Shaoyang University, Hunan 422004, China

Received 7 February 2014; Accepted 24 March 2014; Published 9 April 2014

Academic Editor: Maria N. D. S. Cordeiro

Copyright © 2014 Houqing Zhou. 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

Circulant graphs are an important class of interconnection networks in parallel and distributed computing. In this paper, we discuss the relation of the Wiener index and the Harary index of circulant graphs and the largest eigenvalues of distance matrix and reciprocal distance matrix of circulants. We obtain the following consequence: ; ; , where W, H denote the Wiener index and the Harary index and λ, μ denote the largest eigenvalues of distance matrix and reciprocal distance matrix of circulant graphs, respectively. Moreover we also discuss the Wiener index of nonregular graphs with cut edges.