Table of Contents Author Guidelines Submit a Manuscript
Journal of Chemistry
Volume 2013 (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.

Linked References

  1. G. E. Sharpe, “Solution of the (m+1)-terminal resistive network problem by means of metric geometry,” in Proceedings of the 1st Asilomar Conference on Circuits and Systems, pp. 319–328, Pacific Grove, Calif, USA, November 1967.
  2. G. E. Sharpe, “Theorem on resistive networks,” Electronics Letters, vol. 3, no. 10, pp. 444–445, 1967. View at Publisher · View at Google Scholar
  3. G. E. Sharpe, “Violation of the 2-triple property by resistive networks,” Electronics Letters, vol. 3, no. 12, pp. 543–544, 1967. View at Publisher · View at Google Scholar
  4. A. D. Gvishiani and V. A. Gurvich, “Metric and ultrametric spaces of resistances,” Russian Mathematical Surveys, vol. 42, no. 2, pp. 235–236, 1987. View at Google Scholar
  5. V. Gurvich, “Metric and ultrametric spaces of resistances,” Discrete Applied Mathematics, vol. 158, no. 14, pp. 1496–1505, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. D. J. Klein and M. Randić, “Resistance distance,” Journal of Mathematical Chemistry, vol. 12, no. 1, pp. 81–95, 1993. View at Publisher · View at Google Scholar
  7. P. Y. Chebotarev and E. V. Shamis, “The forest metrics of a graph and their properties,” Automation and Remote Control, vol. 61, no. 8, pp. 1364–1373, 2000. View at Google Scholar · View at Scopus
  8. D. J. Klein and O. Ivanciuc, “Graph cyclicity, excess conductance, and resistance deficit,” Journal of Mathematical Chemistry, vol. 30, no. 3, pp. 271–287, 2001. View at Publisher · View at Google Scholar · View at Scopus
  9. W. Tutte, Connectivity in Graphs, University of Toronto Press, Toronto, Canada, 1966.
  10. D. Bonchev, O. Mekenyan, and N. Trinajstić, “Topological characterization of cyclic structures,” International Journal of Quantum Chemistry, vol. 17, no. 5, pp. 845–893, 1980. View at Publisher · View at Google Scholar
  11. D. Bonchev, A. T. Balaban, X. Liu, and D. J. Klein, “Molecular cyclicity and centricity of polycyclic graphs. I. Cyclicity based on resistance distances or reciprocal distances,” International Journal of Quantum Chemistry, vol. 50, pp. 1–20, 1994. View at Google Scholar
  12. Y. Yang, “Resistance distances and the global cyclicity index of fullerene graphs,” Digest Journal of Nanomaterials and Biostructures, vol. 7, pp. 593–598, 2012. View at Google Scholar
  13. Y. Yang, “On a new cyclicity measure of graphs—the global cyclicity index,” Discrete Applied Mathematics. Accepted.
  14. S. Seshu and M. B. Reed, Linear Graphs and Electrical Networks, Addison-Wesley, Reading, Mass, USA, 1961.
  15. D. M. Cvetković and I. Gutman, “A new spectral method for determining the number of spanning trees,” Publications de l'Institut Mathématique, vol. 29, no. 43, pp. 49–52, 1981. View at Google Scholar
  16. I. Gutman and R. B. Mallion, “On spanning trees in catacondensed molecules,” Zeitschrift für Naturforschung A, vol. 48, no. 10, pp. 1026–1030, 1993. View at Google Scholar
  17. E. J. Farrell, M. L. Gargano, and L. V. Quintas, “Spanning trees in linear polygonal chains,” Bulletin of the ICA, vol. 39, pp. 67–74, 2003. View at Google Scholar