Skip to content
2000
Volume 28, Issue 6
  • ISSN: 1386-2073
  • E-ISSN: 1875-5402

Abstract

Background

The field of nanobiotechnology uses precise nanofabrication techniques to advance our understanding and control of biological systems. Due to their remarkable properties, dendrimers, which are hyperbranched macromolecular structures with distinct and well-defined architectures, have emerged as pivotal entities within this field. They are gaining increasing attention for their potential to catalyze a paradigm shift in medical therapeutics, biotechnological applications, and advanced material sciences.

Objective

This paper focuses on a novel analytical expression and determines the precise value of the augmented Zagreb index, a topological descriptor, for eight classes of nanostar dendrimers.

Methods

The Zagreb index is a topological invariant to predict molecular behaviour and reactivity. In this paper, we have explored its application in characterizing the branching of nanostar dendrimers through computational modelling and mathematical rigor.

Results

Our research has measured the augmented Zagreb index for nanostar dendrimers, which fall into eight distinct classes. The results better explain the relationship between the dendrimers' topology and chemical properties. This correlation has implications for their structural stability and reactivity, potentially leading to new applications.

Conclusion

Developing the augmented Zagreb index for nanostar dendrimers is a significant breakthrough in nanobiotechnology. Based on the correlation between the calculated topological index and the corresponding molecular attributes, our analytical approach has opened up new possibilities for designing and synthesizing dendrimers tailored to specific functions in medical and material science applications. This precise topological quantification could significantly enhance the utility and functionalization of dendrimers in cutting-edge nanotechnological applications.

© 2025 Bentham Science Publishers
Loading

Article metrics loading...

/content/journals/cchts/10.2174/0113862073291384240408074601
2024-04-18
2025-10-06

  • From This Site

    /content/journals/cchts/10.2174/0113862073291384240408074601
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. NieS. XingY. KimG.J. SimonsJ.W. Nanotechnology applications in cancer.Annu. Rev. Biomed. Eng.20079125728810.1146/annurev.bioeng.9.060906.152025 17439359
     [Google Scholar]
  2. SmithD.M. SimonJ.K. BakerJ.R.Jr Applications of nanotechnology for immunology.Nat. Rev. Immunol.201313859260510.1038/nri3488 23883969
     [Google Scholar]
  3. VögtleF. GestermannS. HesseR. SchwierzH. WindischB. Functional dendrimers.Prog. Polym. Sci.2000257987104110.1016/S0079‑6700(00)00017‑4
     [Google Scholar]
  4. NajafiF. Salami-KalajahiM. Roghani-MamaqaniH. A review on synthesis and applications of dendrimers.J. Indian Chem. Soc.202118503517
     [Google Scholar]
  5. NikzamirM. HanifehpourY. AkbarzadehA. PanahiY. Applications of dendrimers in nanomedicine and drug delivery: A review.J. Inorg. Organomet. Polym. Mater.20213162246226110.1007/s10904‑021‑01925‑2
     [Google Scholar]
  6. ChoiJ.W. OhB.K. KimY.K. MinJ. Nanotechnology in biodevices.J. Microbiol. Biotechnol.2007171514 18051347
     [Google Scholar]
  7. DykesG.M. Dendrimers: A review of their appeal and applications.J. Chem. Technol. Biotechnol.200176990391810.1002/jctb.464
     [Google Scholar]
  8. ChauhanA. Dendrimers for drug delivery.Molecules201823493810.3390/molecules23040938 29670005
     [Google Scholar]
  9. TarachP. JanaszewskaA. Recent advances in preclinical research using PAMAM dendrimers for cancer gene therapy.Int. J. Mol. Sci.2021226291210.3390/ijms22062912 33805602
     [Google Scholar]
  10. AstrucD. ChardacF. Dendritic catalysts and dendrimers in catalysis.Chem. Rev.200110192991302410.1021/cr010323t 11749398
     [Google Scholar]
  11. Tabatabaei MirakabadF.S. KhoramgahM.S. KeshavarzF. K.; Tabarzad, M.; Ranjbari, J. Peptide dendrimers as valuable biomaterials in medical sciences.Life Sci.201923311675410.1016/j.lfs.2019.116754 31415768
     [Google Scholar]
  12. ChenZ. DehmerM. Emmert-StreibF. ShiY. Entropy bounds for dendrimers.Appl. Math. Comput.201424246247210.1016/j.amc.2014.05.105
     [Google Scholar]
  13. KlajnertB. BryszewskaM. Dendrimers: Properties and applications.Acta Biochim. Pol.200148119920810.18388/abp.2001_5127 11440170
     [Google Scholar]
  14. UllahA. QasimM. ZamanS. KhanA. Computational and comparative aspects of two carbon nanosheets with respect to some novel topological indices.Ain Shams Eng. J.202213410167210.1016/j.asej.2021.101672
     [Google Scholar]
  15. YamamotoK. HiguchiM. ShikiS. TsurutaM. ChibaH. Stepwise radial complexation of imine groups in phenylazomethine dendrimers.Nature2002415687150951110.1038/415509a 11823855
     [Google Scholar]
  16. GaoW. SiddiquiM.K. ImranM. JamilM.K. FarahaniM.R. Forgotten topological index of chemical structure in drugs.Saudi Pharm. J.201624325826410.1016/j.jsps.2016.04.012 27275112
     [Google Scholar]
  17. HakeemA. Computation of some important degree-based topological indices for Y- graphyne and Zigzag graphyne nanoribbon.Mol. Phys.20232023e221140310.1080/00268976.2023.2211403
     [Google Scholar]
  18. HuilgolM.I. SriramV. BalasubramanianK. Structure–activity relations for antiepileptic drugs through omega polynomials and topological indices.Mol. Phys.20221203e198754210.1080/00268976.2021.1987542
     [Google Scholar]
  19. BačaM. HorváthováJ. MokrišováM. SuhányiováA. SuhànyiovàA. On topological indices of fullerenes.Appl. Math. Comput.201525115416110.1016/j.amc.2014.11.069
     [Google Scholar]
  20. DiudeaM.V. VizitiuA.E. MirzagarM. AshrafiA.R. Sadhhana polynomial in nano- dendrimers.Carpath. J. Math.2010265966
     [Google Scholar]
  21. GhorbaniM. HosseinzadehM.A. Computing index of nanostar dendrimers.Optoelectron. Adv. Mater. Rapid Commun.2010414191422
     [Google Scholar]
  22. GraovacM. Computing fifth geometric–arithmetic index for nanostar dendrimers.J. Math. Nanosci.201113342
     [Google Scholar]
  23. HuiZ. NaeemM. RaufA. AslamA. Predictive ability of physicochemical properties of antiemetic drugs using degree‐based entropies.Int. J. Quantum Chem.202312315e2713110.1002/qua.27131
     [Google Scholar]
  24. HayatS. ImranM. Computation of topological indices of certain networks.Appl. Math. Comput.201424021322810.1016/j.amc.2014.04.091
     [Google Scholar]
  25. RosenK.H. Discrete Mathematics and its applications.7th edNew YorkThe McGraw-Hill Companies2012
     [Google Scholar]
  26. BashirY. AslamA. KamranM. QureshiM. JahangirA. RafiqM. BibiN. MuhammadN. On forgotten topological indices of some dendrimers structure.Molecules201722686710.3390/molecules22060867 28538687
     [Google Scholar]
  27. HusinM. HasniR. ArifN. ImranM. On topological indices of certain families of nanostar dendrimers.Molecules201621782110.3390/molecules21070821 27347913
     [Google Scholar]
  28. CancanM. EdizS. Mutee-Ur-RehmanH. AfzalD. M-polynomial and topological indices Poly (EThyleneAmidoAmine) dendrimers.J. Inform. Optim. Sci.20204141117113110.1080/02522667.2020.1745383
     [Google Scholar]
  29. MunirM. NazeerW. RafiqueS. KangS. M-polynomial and related topological indices of nanostar dendrimers.Symmetry (Basel)2016899710.3390/sym8090097
     [Google Scholar]
  30. BokharyS.A.U.H. ImranM. ManzoorS. On molecular topological properties of dendrimers.Cancer J. Chem.201694212012510.1139/cjc‑2015‑0466
     [Google Scholar]
  31. AlyarS. KhoeilarR. JahanbaniA. Some topological indices of dendrimers.Int. J. Comput. Mater. Sci. Eng.202094205001810.1142/S2047684120500189
     [Google Scholar]
  32. KhabyahA.A. Mathematical aspects and topological properties of two chemical networks.AIMS Math.2023824666468110.3934/math.2023230
     [Google Scholar]
  33. AlaliA.S. AliS. HassanN. MahnashiA.M. ShangY. AssiryA. Algebraic structure graphs over the commutative ring ZM: Exploring Topological indices and entropies using M-Polynomials.Mathematics20231118383310.3390/math11183833
     [Google Scholar]
  34. IrfanM. RehmanH.U. AlmusawaH. RasheedS. BalochI.A. M-polynomials and topological indices for line graphs of chain silicate network and H-Naphtalenic Nanotubes.J. Math.2021202111110.1155/2021/5551825
     [Google Scholar]
  35. ThakareS. ShaikhA. BodasD. GajbhiyeV. Application of dendrimer-based nanosensors in immunodiagnosis.Colloids Surf. B Biointerfaces2022209Pt 211217410.1016/j.colsurfb.2021.112174 34742022
     [Google Scholar]
  36. SoršakE. ValhJ.V. UrekŠ.K. LobnikA. Application of PAMAM dendrimers in optical sensing.Analyst (Lond.)2015140497698910.1039/C4AN00825A 25382859
     [Google Scholar]
  37. FurtulaB. GraovacA. VukičevićD. Augmented Zagreb index.J. Math. Chem.201048237038010.1007/s10910‑010‑9677‑3
     [Google Scholar]
  38. HuangY. LiuB. GanL. Augumented Zagreb index of connected graphs.MATCH Commun. Math. Comput. Chem.201267483494
     [Google Scholar]
  39. NakayamaJ. LinJ.S. An organosilicon dendrimer composed of 16 thiophene rings.Tetrahedron Lett.199738346043604610.1016/S0040‑4039(97)01356‑7
     [Google Scholar]
  40. Yousefi-AzariH. AshrafiA.R. KhalifehM.H. wiener index of organosilicon dendrimer Optoelectron.Adv. Mater. Rapid Comm.201489-10961963
     [Google Scholar]
  41. AlikhaniS. HasniR. ArifN.E. On the atom-bond connectivity index of some families of dendrimers.J. Comput. Theor. Nanosci.20141181802180510.1166/jctn.2014.3570
     [Google Scholar]
/content/journals/cchts/10.2174/0113862073291384240408074601
Loading
Topological Insights into Nanostar Dendrimers by Computing the Augmented Zagreb Index
Comb Chem High Throughput Screen 28, 963 (2025); https://doi.org/10.2174/0113862073291384240408074601
/content/journals/cchts/10.2174/0113862073291384240408074601
/content/journals/cchts/10.2174/0113862073291384240408074601
Loading

Data & Media loading...


  • Article Type:     Research Article
Keyword(s): augmented Zagreb index; molecular topology; nanobiotechnology; nanomaterials science; nanostar dendrimers; Topological index

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error
Please enter a valid_number test