On Eccentricity-Based Topological Descriptors of Dendrimers

Abstract

In the study of QSAR/QSPR, eccentric connectivity index has a prominent place among the other topological indices, due to its high degree of predictability of pharmaceutical properties. In this paper, we compute the exact formulas of eccentric connectivity index and its corresponding polynomial, total eccentric connectivity index and its corresponding polynomial, Zagreb eccentricity indices, the augmented eccentric connectivity index, modified eccentric connectivity index and its corresponding polynomial and the edge version of the eccentric connectivity index for a class of perylenediimide-cored (PDI-cored) dendrimers.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2

References

  1. Alaeiyan M, Asadpour J, Mojarad R (2013) A numerical method for MEC polynomial and MEC index of one-pentagonal carbon nanocones. Fuller Nanotub Carbon Nanostruct 21(10):825–835

    Article  Google Scholar 

  2. Ashrafi AR, Ghorbani M, Jalali M (2009) Eccentric connectivity polynomial of an infinite family of fullerenes. Optoelectron Adv Mater Rapid Commun 3(8):823–826

    Google Scholar 

  3. Ashrafi AR, Ghorbani M, Hossein-Zadeh MA (2011) The eccentric connectivity polynomial of some graph operations. Serdica J Comput 5:101–116

    MathSciNet  MATH  Google Scholar 

  4. Bajaj S, Sambi SS, Gupta S, Madan AK (2006) Model for prediction of anti-HIV activity of 2-pyridinone derivatives using novel topological descriptor. QSAR Comb Sci 25:813–823

    Article  Google Scholar 

  5. De N (2013) Relationship between augmented eccentric connectivity index and some other graph invariants. Int J Adv Math Sci 1(2):26–32

    Google Scholar 

  6. Došlić T, Saheli M (2011) Augmented eccentric-connectivity index. Miskolc Math Notes 12(2):149–157

    MathSciNet  Article  MATH  Google Scholar 

  7. Dureja H, Madan AK (2005) Topochemical models for prediction of cyclin-dependent kinase 2 inhibitory activity of indole-2-ones. J Mol Graph Model 11:525–531

    Article  Google Scholar 

  8. Ghorbani M, Hossein-Zadeh MA (2012) A new version of Zagreb indices. Filomat 26:93–100

    MathSciNet  Article  MATH  Google Scholar 

  9. Gopalan SS, Yarema KJ (2007) Nanotechnologies for the life sciences: dendrimers in cancer treatment and diagnosis. Wiley, New York

    Google Scholar 

  10. Gupta S, Singh M, Madan AK (2000) Connective eccentricity index: a novel topological descriptor for predicting biological activity. J Mol Graph Model 18:18–25

    Article  Google Scholar 

  11. Gupta S, Singh M, Madan AK (2002) Application of graph theory: relationship of eccentric connectivity index and Wiener’s index with anti-inflammatory activity. J Math Anal Appl 266:259–268

    MathSciNet  Article  MATH  Google Scholar 

  12. Ilic A, Gutman I (2011) Eccentric connectivity index of chemical trees. MATCH Commun Math Comput Chem 65:731–744

    MathSciNet  MATH  Google Scholar 

  13. Kumar V, Madan AK (2005) Application of graph theory: prediction of glycogen synthase kinase-3 beta inhibitory activity of thiadiazolidinones as potential drugs for the treatment of Alzheimer’s disease. Eur J Pharm Sci 24:213–218

    Article  Google Scholar 

  14. Kumar V, Madan AK (2006) Application of graph theory: prediction of cytosolic phospholipase A2 inhibitory activity of propan-2-ones. J Math Chem 39:511–521

    MathSciNet  Article  MATH  Google Scholar 

  15. Lather V, Madan AK (2005) Topological models for the prediction of HIV-protease inhibitory activity of tetrahydropyrimidin-2-ones. J Mol Graph Model 23:339–345

    Article  Google Scholar 

  16. Liu K, Xu Z, Yin M (2015) Perylenediimide-cored dendrimers and their bioimaging and gene delivery applications. Prog Polym Sci 46:25–54

    Article  Google Scholar 

  17. Odaba ZN (2013) The edge eccentric-connectivity index of dendrimers. J Comput Theor Nanosci 10(4):783–784

    Article  Google Scholar 

  18. Sardana S, Madan AK (2001) Application of graph theory: relationship of molecular connectivity index, Wiener index and eccentric connectivity index with diuretic activity. MATCH Commun Math Comput Chem 43:85–98

    MathSciNet  MATH  Google Scholar 

  19. Sardana S, Madan AK (2003) Topological models for prediction of antihypertensive activity of substituted benzylimidazoles. J Mol Struct (Theochem) 638:41–49

    Article  Google Scholar 

  20. Sharma V, Goswami R, Madan AK (1997) Eccentric connectivity index: a novel highly discriminating topological descriptor for structure–property and structure–activity studies. J Chem Inf Comput Sci 37:273–282

    Article  Google Scholar 

  21. Suresh R, Singh C, Rewar P (2015) Dendrimers as carriers and its application in therapy. Int J Anal Pharm Biomed Sci 4(3):15–23

    Google Scholar 

  22. Tomalia DA, Baker H, Dewald JR, Hall M, Kallos G, Martin S, Roeck J, Ryder J, Smith P (1986) Dendritic macromolecules: synthesis of starburst dendrimers. Macromolecules 19:2466–2468

    Article  Google Scholar 

  23. Wiener H (1947) Structural determination of paraffin boiling points. J Am Chem Soc 69(1):17–20

    Article  Google Scholar 

  24. Xu X, Guo Y (2012) The edge version of eccentric-connectivity index. Int Math Forum 7(6):273–280

    MathSciNet  MATH  Google Scholar 

  25. Xu Z, He B, Shen J, Yang W, Yin M (2013) Fluorescent water-soluble perylenediimide-cored cationic dendrimers: synthesis, optical properties, and cell uptake. Chem Commun 49:3646–3648

    Article  Google Scholar 

  26. Zhou B, Du Z (2010) On eccentric connectivity index. MATCH Commun Math Comput Chem 63:181–198

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Muhammad Aamir.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Iqbal, Z., Ishaq, M. & Aamir, M. On Eccentricity-Based Topological Descriptors of Dendrimers. Iran J Sci Technol Trans Sci 43, 1523–1533 (2019). https://doi.org/10.1007/s40995-018-0621-x

Download citation

Keywords

  • Eccentric connectivity index
  • Total eccentric connectivity index
  • Zagreb eccentric connectivity indices
  • Augmented eccentric connectivity index
  • PDI-cored dendrimers