Table of Contents
Journal of Discrete Mathematics
Volume 2014, Article ID 292679, 5 pages
http://dx.doi.org/10.1155/2014/292679
Research Article

Eccentric Connectivity and Zagreb Coindices of the Generalized Hierarchical Product of Graphs

1Department of Mathematics, Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran
2Department of Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan 87317-51167, Iran

Received 9 May 2014; Accepted 14 October 2014; Published 27 November 2014

Academic Editor: Aleksandar Ilić

Copyright © 2014 M. Tavakoli 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. I. Gutman and N. Trinajstić, “Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons,” Chemical Physics Letters, vol. 17, no. 4, pp. 535–538, 1972. View at Publisher · View at Google Scholar · View at Scopus
  2. I. Gutman and K. C. Das, “The first Zagreb index 30 years after,” MATCH: Communications in Mathematical and in Computer Chemistry, no. 50, pp. 83–92, 2004. View at Google Scholar · View at MathSciNet · View at Scopus
  3. S. Nikolić, G. Kovačević, A. Milićević, and N. Trinajstić, “The Zagreb indices 30 years after,” Croatica Chemica Acta, vol. 76, no. 2, pp. 113–124, 2003. View at Google Scholar
  4. A. R. Ashrafi, T. Došlic, and A. Hamzeh, “Extremal graphs with respect to the Zagreb coindices,” MATCH: Communications in Mathematical and in Computer Chemistry, vol. 65, no. 1, pp. 85–92, 2011. View at Google Scholar · View at MathSciNet · View at Scopus
  5. Y. Guo, Y. Du, and Y. Wang, “Bipartite graphs with extreme values of the first general Zagreb index,” MATCH: Communications in Mathematical and in Computer Chemistry, vol. 63, no. 2, pp. 469–480, 2010. View at Google Scholar · View at MathSciNet · View at Scopus
  6. 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 MathSciNet · View at Scopus
  7. M. H. Khalifeh, H. Yousefi-Azari, and A. R. Ashrafi, “The first and second Zagreb indices of some graph operations,” Discrete Applied Mathematics, vol. 157, no. 4, pp. 804–811, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. T. Došlić, “Vertex-weighted Wiener polynomials for composite graphs,” Ars Mathematica Contemporanea, vol. 1, no. 1, pp. 66–80, 2008. View at Google Scholar · View at MathSciNet
  9. A. R. Ashrafi, T. Došlić, and A. Hamzeh, “The Zagreb coindices of graph operations,” Discrete Applied Mathematics, vol. 158, no. 15, pp. 1571–1578, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. V. Sharma, R. Goswami, and A. K. Madan, “Eccentric connectivity index: a novel highly discriminating topological descriptor for structure-property and structure-activity studies,” Journal of Chemical Information and Computer Sciences, vol. 37, no. 2, pp. 273–282, 1997. View at Google Scholar · View at Scopus
  11. A. Ilić, “Eccentric connectivity index,” in Novel Molecular Structure Descriptors—Theory and Applications II, I. Gutman and B. Furtula, Eds., pp. 139–168, University of Kragujevac, Kragujevac, Serbia, 2010. View at Google Scholar
  12. L. Barrière, F. Comellas, C. Dalfó, and M. A. Fiol, “The hierarchical product of graphs,” Discrete Applied Mathematics, vol. 157, no. 1, pp. 36–48, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. L. Barrière, C. Dalfó, M. A. Fiol, and M. Mitjana, “The generalized hierarchical product of graphs,” Discrete Mathematics, vol. 309, no. 12, pp. 3871–3881, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. M. Arezoomand and B. Taeri, “Applications of generalized hierarchical product of graphs in computing the Szeged index of chemical graphs,” MATCH: Communications in Mathematical and in Computer Chemistry, vol. 64, no. 3, pp. 591–602, 2010. View at Google Scholar · View at MathSciNet · View at Scopus
  15. M. Arezoomand and B. Taeri, “Zagreb indices of the generalized hierarchical product of graphs,” MATCH: Communications in Mathematical and in Computer Chemistry, vol. 69, no. 1, pp. 131–140, 2013. View at Google Scholar · View at MathSciNet · View at Scopus
  16. M. Tavakoli, F. Rahbarnia, and A. R. Ashrafi, “Further results on hierarchical product of graphs,” Discrete Applied Mathematics, vol. 161, no. 7-8, pp. 1162–1167, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. R. Hammack, W. Imrich, and S. Klavžar, Handbook of Product Graphs, Taylor & Francis, 2nd edition, 2011. View at MathSciNet
  18. K. Pattabiraman and P. Paulraja, “Vertex and edge Padmakar-Ivan indices of the generalized hierarchical product of graphs,” Discrete Applied Mathematics, vol. 160, no. 9, pp. 1376–1384, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. B. Eskender and E. Vumar, “Eccentric connectivity index and eccentric distance sum of some graph operations,” Transactions on Combinatorics, vol. 2, no. 1, pp. 103–111, 2013. View at Google Scholar · View at MathSciNet