Skip to main content
Log in

The Edge Versions of Degree-Based Topological Descriptors of Dendrimers

  • Original Paper
  • Published:
Journal of Cluster Science Aims and scope Submit manuscript

Abstract

In the study of the quantitative structure–activity relationship and quantitative structure–property relationships, degree-based topological indices are the most prominent and can be used to characterize the chemical compounds and predict their certain physiochemical properties like molecular weight, boiling point, refractive index, density, etc. Dendrimers are highly branched, star-shaped macromolecules with nanometer-scale dimensions. Dendrimers are defined by three components: a central core, an interior dendritic structure (the branches), and an exterior surface with functional surface groups. In this paper, we compute closed formulae of edge versions of forgotten index, Hyper-Zagreb index, sum-connectivity index, harmonic index, augmented Zagreb index and Randić index for fluorescent water-soluble PDI-cored cationic dendrimers and trizane based dendrimers.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. P. S. Kumar, M. S. Datta, D. M. Kumar, T. V. Kumar, V. K. Kr and D. Ram (2016). J. drug deliv. ther. 6, (2), 71.

    CAS  Google Scholar 

  2. E. Abbasi, S. F. Aval, A. Akbarzadeh, M. Milani, H. T. Nasrabadi, S. W. Joo, et al. (2014). Nanoscale Res. Lett. 9, 247.

    Article  Google Scholar 

  3. J. A. Bondy and U. S. R. Murty Graph Theory with Applications (Springer, Berlin, 2008).

    Google Scholar 

  4. I. Gutman and N. Trinajstić (1972). Chem. Phys. Lett. 17, 535.

    Article  CAS  Google Scholar 

  5. B. Furtula and I. Gutman (2015). J. Math. Chem. 53, (4), 1184.

    Article  CAS  Google Scholar 

  6. V. R. Kulli (2017). Ann. Pure Appl. Math. 14, (3), 449.

    Article  Google Scholar 

  7. G. H. Shirdel, H. Rezapour and A. M. Sayadi (2013). Iran. J. Math. Chem. 4, 213.

    Google Scholar 

  8. X. J. Zhang, W. Sajjad, A. Q. Baig and M. R. Farahani (2017). Appl. Math. 8, 1445.

    Article  Google Scholar 

  9. B. Zhou and N. Trinajstić (2009). J. Math. Chem. 46, 1252.

    Article  CAS  Google Scholar 

  10. L. Zhong (2012). Appl. Math. Lett. 25, 561.

    Article  Google Scholar 

  11. R. Nazir, S. Sardar, S. Zafar and Z. Zahid (2016). J. Appl. Math. Inf. 34, 479.

    Google Scholar 

  12. B. Furtula, A. Graovac and D. Vukicevic (2010). J. Math. Chem. 48, 370.

    Article  CAS  Google Scholar 

  13. M. Randić (1975). J. Amer. Chem. Soc. 97, 6609.

    Article  Google Scholar 

  14. Y. Gao, W. Sajjad, A. Q. Baig and M. R. Farahani (2017). Int. J. Pure Appl. Math115, (2), 405.

    Google Scholar 

  15. A. Aslam, Y. Bashir, S. Ahmed and W. Gao (2017). Z. Naturforsch. 72, 559.

    Article  CAS  Google Scholar 

  16. A. Aslam, M. K. Jamil, W. Gao and W. Nazeer (2018). Nanotechnol. Rev. 7, 123.

    Article  CAS  Google Scholar 

  17. Y. Bashir, A. Aslam, M. Kamran, I. Qureshi, A. Jahangir, M. Rafiq, N. Bibi and N. Muhammad (2017). Molecules22, 867.

    Article  Google Scholar 

  18. A. Aslam, S. Ahmad, W. Gao (2017). Z. Naturforsch.72, 711.

    Article  CAS  Google Scholar 

  19. W. Gao, Z. Iqbal, M. Ishaq, R. Sarfraz, M. Aamir and A. Aslam (2018). Biomolecules8, 71.

    Article  Google Scholar 

  20. I. Gutman (2013). Croat. Chem. Acta. 86, 351–361.

    Article  CAS  Google Scholar 

  21. M. Imran, M. K. Siddiqui, M. Naeem and M. A. Iqbal (2018). Symmetry10, 1–21.

    Google Scholar 

  22. M. Imran, M. A. Ali, S. Ahmad, M. K. Siddiqui and A. Q. Baig (2018). Symmetry10, (6), 1–20.

    Google Scholar 

  23. Z. Iqbal, M. Ishaq and R. Farooq (2017). J. Inf. Math. Sci. 9, (1), 217.

    Google Scholar 

  24. Z. Iqbal, M. Ishaq and M. Aamir (2018). Iran. J. Sci. Technol. Trans. Sci. https://doi.org/10.1007/s40995-018-0621-x.

    Article  Google Scholar 

  25. S. M. Kang, Z. Iqbal, M. Ishaq, R. Sarfraz, A. Aslam and W. Nazeer (2018). Symmetry10, 237.

    Article  Google Scholar 

  26. Z. Xu, B. He, J. Shen, W. Yang and M. Yin (2013). Chem. Commun. 49, 3646.

    Article  CAS  Google Scholar 

  27. D. G. Gajjar, R. M. Patel, H. N. Patel and P. M. Patel (2015). Am. J. Polym. Sci. Eng. 3, 73–89.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Adnan Aslam.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Iqbal, Z., Aslam, A., Ishaq, M. et al. The Edge Versions of Degree-Based Topological Descriptors of Dendrimers. J Clust Sci 31, 445–452 (2020). https://doi.org/10.1007/s10876-019-01658-w

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10876-019-01658-w

Keywords

Navigation