Study of Dendrimers by Topological Indices

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In this paper, five degree based topological indices, the first Zagreb (M1), second Zagreb (M2), first multiple Zagreb (PM1), second multiple Zagreb (PM2), and the hyper Zagreb (HM) indices of two types of dendrimers are studied. In addition, two distance based topological indices, the total eccentricity (θ) and eccentric connectivity (ξc) indices of these dendrimers are computed.


  • 1. Buhleier, E.; Wehner, W.; Vögtle, F. Cascade and nonskid-chain-like synthesis of molecular cavity topologies. Synthesis. 1978, 2, 155-158.

  • 2. Tomalia, D. A.; Baker, H.; Dewald, J.; Hall, M.; Kallos, G.; Martin, S.; Roeck, J.; Ryder, J.; Smith, P. A new class of polymers: Starburst-dendritic macromolecules. Polym. J. 1985, 17, 117-132.

  • 3. Diudea, M. V.; Katona, G. Molecular Topology of Dendrimers, in: G. A. Newkome, Ed. Advan. Dendritic Macromol. 1999, 4, 135-201.

  • 4. Newkome, G. R.; Moorefield, C. N.; Vögtle, F. Dendrimers and Dendrons, Wiley-VCH Verlag GmbH & Co. KGaA. 2002.

  • 5. Farahani, M. R.; Gao, W.; Kanna, R. M. R. The connective eccentric index for an infinite family of dendrimers. Indian Journal of Fundamental and Applied Life Sciences. 2015, 5 (S4), 766-771.

  • 6. Soleimani, N.; Mohseni, E.; Helalbin, S. Theoretical study of nanostar dendrimers. Studia Universitatis Babes-Bolyai, Chemia. 2016, 1, 127-140.

  • 7. Soleimani, N.; Mohseni, E.; Maleki, N. Connectivity indices of some famous dendrimers. Journal of Chemical and Pharmaceutical Research. 2016, 8(8), 229-235.

  • 8. Soleimani, N.; Nikmehr, M. J.; Tavallaee, H. A. Computation of the different topological indices of nanostructures. Journal of the national science foundation of Sri Lanka. 2015, 43(2), 127-133.

  • 9. Nejati, A.; Alaeiyan, M. The edge version of MEC index of one-pentagonal carbon nanocones. Bulgarian Chemical Communications, 2014, 46(3), 462-464.

  • 10. Nikmehr, M. J.; Soleimani, N. Computing energy and some toplogical indices of Г(n), Mathematics and Computer Science, 2016, 1(4), 101-107.

  • 11. Nikmehr, M. J.; Soleimani, N.; Tavallaee, H. A. Computing some topological indices of carbon nanotubes. Proceedings of the Institute of Applied Mathematics. 2015, 4(1), 20-25.

  • 12. Nikmehr, M. J.; Veylaki, M.; Soleimani, N. Some topological indices of V-Phenylenic nanotube and nanotori. Optoelectron. Adv. Mater.-Rapid Comm. 2015, 9(9), 1147-1149.

  • 13. Nikmehr, M. J.; Heidarzadeh, L.; Soleimani, N. Calculating different topological indices of total graph of Zn. Studia Scientiarum Mathematicarum Hungarica. 2014, 51(1), 133-140.

  • 14. Ghorbani, M.; Jalali, M. A simple algorithm for computing topological indices of dendrimers. Iranian Journal of Mathematical Sciences and Informatics. 2007, 2(2), 17-23.

  • 15. Buckley, F.; Harary, F. Distance in Graphs. Addison-Wesley, Reading. 1990.

  • 16. Todeschini, R.; Consonni, V. Handbook of Molecular Descriptors. Weinheim, Wiley-VCH. 2000.

  • 17. Gutman, I.; Das, K. C. Some properties of the second zagreb index. MATCH Commun. Math. Comput. Chem. 2004, 50, 103-112.

  • 18. Ghorbani, M.; Hemmasi, M. Eccentric connectivity polynomial of C12n+4 Fullerenes. Digest Journal of Nanomaterials and Biostructures. 2009, 4, 545-547.

  • 19. Ashrafi, A. R.; Ghorbani, M.; Hossein-Zadeh, M. A. The eccentric connectivity polynomial of some graph operations. Serdica J. Computing. 2011, 5, 101-116.

  • 20. Gutman, I.; Trinajstić, N. Graph theory and molecular orbitals, Total π-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 1972, 17, 535-538.

  • 21. Gutman, I. Multiplicative Zagreb indices of trees. Bulletin of the Veterinary Institute in Pulawy. 2011, 1, 13-19.

  • 22. Ghorbani, M.; Azimi, N. Note on multiple Zagreb indices. Iranian Journal of Mathematical Chemistry. 2012, 3, 137-143.

  • 23. Shirdel, G. H.; Rezapour, H.; Sayadi, A. M. The Hyper-Zagreb index of graph operations. Iranian Journal of Mathematical Chemistry. 2013, 4(2), 213-220.

  • 24. Sharma, V.; Goswami, R.; Madan, A. K. Eccentric connectivity index: A novel highly discriminating topological descriptor for structure–property and structure–activity studies. J. Chem. Inf. Comput. Sci. 1997, 37, 273-282.

  • 25. Ashrafi, A. R.; Saheli, M.; Ghorbani, M. The eccentric connectivity index of nanotubes and nanotori. Journal of Computational and Applied Mathematics. 2011, 235(16), 4561-4566.

  • 26. De, N.; Pal, A.; Nayeem, S. M. A. Total eccentricity index of some composite graphs. Malaya J. Mat. 2015, 3(4), 523-529.

  • 27. De, N.; Nayeem, S. M. A.; Pal, A. Connective eccentricity index of some thorny graphs. Ann. Pure Appl. Math. 2014, 7(1), 59-64.

  • 28. Doslić, T.; Ghorbani, M.; Hosseinzadeh, M. A. Eccentric connectivity polynomial of some graph operations. Utilitas Mathematica. 2011, 84, 297-309.

  • 29. Nantalaksakul, A.; Reddy, D. R.; Bardeen, C. J.; Thayumanavan, S. Light harvesting dendrimers. Photosynthesis Research. 2006, 87, 133-150.

  • 30. Fréchet, J. M. J.; Tomalia, D. A. Introduction to the Dendritic state: Dendrimers and other Dendritic Polymers. John Wiley and Sons Ltd. 2001, 24-23.

  • 31. Diudea, M. V.; Ursu, O.; Nagy, Cs. L. TOPOCLUJ, Babes-Bolyai University, Cluj. 2002.

Acta Chemica Iasi

The Journal of "Alexandru Ioan Cuza" University from Iasi

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