Skip to main content
Log in

The third and hyper-Zagreb coindices of some graph operations

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

Abstract

In this paper some basic mathematical properties for the third and hyper Zagreb coindices of graph operations containing the Cartesian product and composition will be explained.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Ashrafi, A.R., Doslić, T., Hamzeh, A.: The Zagreb coindices of graph operations. Discret. Appl. Math. 158, 1571–1578 (2010)

    Article  MATH  Google Scholar 

  2. Braun, J., Kerber, A., Meringer, M., Rucker, C.: Similarity of molecular descriptors: the equivalence of Zagreb indices and walk counts. MATCH Commun. Math. Comput. Chem. 54, 163–176 (2005)

    MathSciNet  MATH  Google Scholar 

  3. Diudea, M.V., Gutman, I., Jantschi, L.: Molecular Topology. Huntington, New York (2001)

    Google Scholar 

  4. Dobrynin, A.A., Gutman, I., Klavzar, S., Zigert, P.: Wiener index of hexagonal systems. Acta Appl. Math. 72, 247–294 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Dobrynin, A.A., Entringer, R., Gutman, I.: Wiener index of trees: theory and applications. Acta Appl. Math. 66, 211–249 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. Doslić, T.: Vertex-weighted Wiener polynomials for composite graphs. Ars Math. Contemp. 1, 66–80 (2008)

    MathSciNet  Google Scholar 

  7. Fath-Tabar, G.H.: Old and new Zagreb indices of graphs. MATCH Commun. Math. Comput. Chem. 65, 79–84 (2011)

    MathSciNet  MATH  Google Scholar 

  8. Graovać, A., Pisanski, T.: On the Wiener index of a graph. J. Math. Chem. 8, 53–62 (1991)

    Article  MathSciNet  Google Scholar 

  9. Gutman, I., Das, K.C.: The first Zagreb index 30 years after. MATCH Commun. Math. Comput. Chem. 50, 83–92 (2004)

    MathSciNet  MATH  Google Scholar 

  10. Harary, F.: Graph Theory. Addison-Wesley, Reading, MA (1969)

    Google Scholar 

  11. Imrich, W., Klavzar, S.: Product Graphs: Structure and Recognition. John Wiley & Sons, New York (2000)

    Google Scholar 

  12. Khalifeh, M.H., Yousefi-Azari, H., Ashrafi, A.R.: The hyper-Wiener index of graph operations. Comput. Math. Appl. 56, 1402–1407 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Khalifeh, M.H., Yousefi-Azari, H., Ashrafi, A.R.: The first and second Zagreb indices of some graph operations. Discret. Appl. Math. 157, 804–811 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  14. Nikmehr, M.J., Heidarzadeh, L., Soleimani, N.: Calculating different topological indices of total graph of \(\mathbb{Z}_n \). Studia Sci. Math. Hung. 51(1), 133–140 (2014)

    MATH  Google Scholar 

  15. Nikmehr, M.J., Soleimani, N., Veylaki, M.: Topological indices based end-vertex degrees of edges on nanotubes. Proc. Inst. Appl. Math. 3(1), 89–97 (2014). (to appear)

    Google Scholar 

  16. Nikolic, S., Kovacevic, G., Milicevic, A., Trinajstic, N.: The Zagreb indices 30 years after. Croat. Chem. Acta. 76, 113–124 (2003)

    Google Scholar 

  17. Sagan, B.E., Yeh, Y.N., Zhang, P.: The Wiener polynomial of a graph. Int. J. Quant. Chem. 60(5), 959–969 (1996)

    Article  Google Scholar 

  18. Shirdel, G.H., Rezapour, H., Sayadi, A.M.: The Hyper-Zagreb Index of Graph Operations. Iran. J. Math. Chem. 4(2), 213–220 (2013)

    Google Scholar 

  19. Stevanović, D.: Hosoya polynomials of composite graphs. Discret. Math. 235, 237–244 (2001)

    Article  MATH  Google Scholar 

  20. Trinajstić, N.: Chemical Graph Theory. CRC Press, Boca Raton, FL (1992)

    Google Scholar 

  21. West, D.B.: Introduction to Graph Theory. Prentice Hall, Upper Saddle River (1996)

    MATH  Google Scholar 

  22. Wiener, H.: Structural determination of the paraffin boiling points. J. Am. Chem. Soc. 69, 17–20 (1947)

    Article  Google Scholar 

  23. Zhou, B.: Zagreb indices. MATCH Commun. Math. Comput. Chem. 52, 113–118 (2004)

    MATH  Google Scholar 

  24. Zhou, B., Gutman, I.: Further properties of Zagreb indices. MATCH Commun. Math. Comput. Chem. 54, 233–239 (2005)

    MathSciNet  MATH  Google Scholar 

  25. Zhou, B., Gutman, I.: Relations between Wiener, hyper-Wiener and Zagreb indices. Chem. Phys. Lett. 394, 93–95 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Maryam Veylaki.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Veylaki, M., Nikmehr, M.J. & Tavallaee, H.A. The third and hyper-Zagreb coindices of some graph operations. J. Appl. Math. Comput. 50, 315–325 (2016). https://doi.org/10.1007/s12190-015-0872-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-015-0872-z

Keywords

Mathematics Subject Classification

Navigation