Table of Contents
International Journal of Combinatorics
Volume 2014, Article ID 696507, 4 pages
http://dx.doi.org/10.1155/2014/696507
Research Article

The Terminal Hosoya Polynomial of Some Families of Composite Graphs

1Polytechnic Institute of New York University, Brooklyn, NY 11201, USA
2Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Avenida Països Catalans 26, 43007 Tarragona, Spain

Received 27 December 2013; Accepted 31 March 2014; Published 16 April 2014

Academic Editor: Jiang Zeng

Copyright © 2014 Emeric Deutsch and Juan Alberto Rodríguez-Velázquez. 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. A. A. Dobrynin, R. Entringer, and I. Gutman, “Wiener index of trees: theory and applications,” Acta Applicandae Mathematicae. An International Survey Journal on Applying Mathematics and Mathematical Applications, vol. 66, no. 3, pp. 211–249, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. H. Hosoya, “On some counting polynomials in chemistry,” Discrete Applied Mathematics, vol. 19, no. 1–3, pp. 239–257, 1988. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. B. E. Sagan, Y. Yeh, and P. Zhang, “The Wiener polynomial of a graph,” International Journal of Quantum Chemistry, vol. 60, no. 5, pp. 959–969, 1996. View at Google Scholar · View at Scopus
  4. G. G. Cash, “Relationship between the Hosoya polynomial and the hyper-Wiener index,” Applied Mathematics Letters, vol. 15, no. 7, pp. 893–895, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. I. Gutman, Y. Zhang, M. Dehmer, and A. Ilic, “Altenburg, Wiener, and Hosoya polynomials,” in Distance in Molecular Graphs-Theory, I. Gutman and B. Furtula, Eds., pp. 49–70, University of Kragujevac, Kragujevac, Serbia, 2012. View at Google Scholar
  6. E. Estrada, O. Ivanciuc, I. Gutman, A. Gutierrez, and L. Rodríguez, “Extended Wiener indices. A new set of descriptors for quantitative structure-property studies,” New Journal of Chemistry, vol. 22, no. 8, pp. 819–822, 1998. View at Google Scholar · View at Scopus
  7. E. Deutsch and S. Klavžar, “Computing the Hosoya polynomial of graphs from primary subgraphs,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 70, no. 2, pp. 627–644, 2013. View at Google Scholar · View at MathSciNet
  8. I. Gutman, B. Furtula, and M. Petrović, “Terminal Wiener index,” Journal of Mathematical Chemistry, vol. 46, no. 2, pp. 522–531, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. L. A. Székely, H. Wang, and T. Wu, “The sum of the distances between the leaves of a tree and the “semi-regular” property,” Discrete Mathematics, vol. 311, no. 13, pp. 1197–1203, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. X. Deng and J. Zhang, “Equiseparability on terminal Wiener index,” Applied Mathematics Letters, vol. 25, no. 3, pp. 580–585, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Y.-H. Chen and X.-D. Zhang, “On Wiener and terminal Wiener indices of trees,” MATCH Communications in Mathematical and in Computer Chemistry, vol. 70, no. 2, pp. 591–602, 2013. View at Google Scholar · View at MathSciNet
  12. K. P. Narayankar, S. S. Shirkol, H. S. Ramane, and S. B. Lokesh, “Terminal Hosoya polynomial of thorn graphs,” in International Conference on Discrete Mathematics (ICDM '13), Karnatak University, Dharwad, India, 2013.
  13. H. S. Ramane, A. B. Ganagi, K. P. Narayankar, and S. S. Shirkol, “Terminal Hosoya polynomial of line graphs,” Journal of Discrete Mathematics, vol. 2013, Article ID 857908, 3 pages, 2013. View at Publisher · View at Google Scholar
  14. C. D. Godsil and B. D. McKay, “A new graph product and its spectrum,” Bulletin of the Australian Mathematical Society, vol. 18, no. 1, pp. 21–28, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. A. J. Schwenk, “Computing the characteristic polynomial of a graph,” in Graphs and Combinatorics, R. Bari and F. Harary, Eds., pp. 153–172, Springer, Berlin, Germany, 1974. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. R. Frucht and F. Harary, “On the corona of two graphs,” Aequationes Mathematicae, vol. 4, pp. 322–325, 1970. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. D. Stevanović, “Hosoya polynomial of composite graphs,” Discrete Mathematics, vol. 235, no. 1–3, pp. 237–244, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet