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Journal of Chemistry
Volume 2013, Article ID 483962, 5 pages
http://dx.doi.org/10.1155/2013/483962
Research Article

The Global Cyclicity Index of Benzenoid Chains

1School of Mathematics and Information Science, Yantai University, Yantai, Shandong 264005, China
2School of Mathematics, Shandong University, Jinan, Shandong 250010, China

Received 28 May 2013; Accepted 20 September 2013

Academic Editor: Arturo Espinosa

Copyright © 2013 Yujun Yang 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 resistance distance between vertices and of a connected (molecular) graph is computed as the effective resistance between nodes and in the corresponding network constructed from by replacing each edge of with a unit resistor. The conductance excess between any and of is the difference between and the reciprocal of the distance between and . The global cyclicity index of is defined as the sum of conductance excesses between all pairs of adjacent vertices. In this paper, by computing resistance distances between pairs of adjacent vertices in linear polyacenes, an explicit formula for the global cyclicity index of a benzenoid chain is obtained in terms of its number of hexagons.