SpringerLink
Log in

Weighted bond-additive descriptors of titanium oxide nanosheet

  • Regular Article
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

Titanium oxide nanosheets are low-dimensional nanostructures of titanium oxide with various unique properties. These nanostructures have significant possible applications in optics, electronics, photocatalysis, gas sensing, drug design, and so on. Weighted bond-additive descriptors quantify the peripherality measure of molecular graphs and also analyze the remarkable bond affinity properties compared with Szeged-type descriptors. This paper explores the handy formulae of weighted bond-additive descriptors of two-dimensional titanium oxide nanosheets, which is the extensive analysis from the literatures of bond additive descriptors such as Szeged, edge Szeged, Padmakar–Ivan, edge Padmakar–Ivan, Mostar, and edge Mostar. Moreover, the relationships between different weighted bond-additive descriptors in titanium oxide nanosheets are investigated.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data availability

The authors confirm that the data supporting the findings of this study are available within the article.

References

  1. A. Prathik, K. Uma, J. Anuradha, An overview of application of graph theory. Int. J. ChemTech Res. 9(2), 242–248 (2016)

    Google Scholar 

  2. K. Balasubramanian, Combinatorics, big data, neural network & AI for medicinal chemistry & drug administration. Lett. Drug. Des. Discov. 18(10), 943–948 (2021)

    Article  Google Scholar 

  3. M.I. Huilgol, V. Sriram, K. Balasubramanian, Structure-activity relations for antiepileptic drugs through omega polynomials and topological indices. Mol. Phys. 119(24), e1987542 (2021)

    Google Scholar 

  4. K. Balasubramanian, Computational and artificial intelligence techniques for drug discovery and administration, Reference Module in Biomedical Sciences, Elsevier, Amsterdam, (2021)

  5. K. Balasubramanian, Mathematical and computational techniques for drug discovery: promises and developments. Curr. Top. Med. Chem. 18(32), 2774–2799 (2018)

    Article  Google Scholar 

  6. L. Abdel-Ilah, E. Veljović, L. Gurbeta, A. Badnjević, Applications of QSAR study in drug design. Int. J. Eng. Res. 6(6), (2017)

  7. H. González-Diáz, S. Vilar, L. Santana, E. Uriarte, Medicinal chemistry and bioinformatics - current trends in drugs discovery with networks topological indices. Curr. Top. Med. Chem. 7(10), 1015–1029 (2007)

    Article  Google Scholar 

  8. F. Emmert-Streib, M. Dehmer, Networks for systems biology: Conceptual connection of data and function. IET Syst. Biol. 5(3), 185–207 (2011)

    Article  Google Scholar 

  9. R.E. Ulanowicz, Information theory in ecology. Comput. Chem. 25(4), 393–399 (2001)

    Article  Google Scholar 

  10. T. Wilhelm, J. Hollunder, Information theoretic description of networks. Phys. A: Stat. Mech. Appl. 388(1), 385–396 (2007)

    Article  MathSciNet  Google Scholar 

  11. S. Klavžar, M.J. Nadjafi-Arani, Cut method: Update on recent developments and equivalence of independent approaches. Curr. Org. Chem. 19(4), 348–358 (2015)

    Article  Google Scholar 

  12. M.J. Nadjafi-Arani, S. Klavžar, Cut method and Djoković–Winkler’s relation. Electron. Notes Discr. Math. 45, 153–157 (2014)

    Article  MATH  Google Scholar 

  13. S. Klavžar, I. Gutman, B. Mohar, Labeling of benzenoid systems which reflects the vertex-distance relations. J. Chem. Inf. Model. 35(3), 590–593 (1995)

    Google Scholar 

  14. A. Ghicov, H. Tsuchiya, J.M. Macak, P. Schmuki, Titanium oxide nanotubes prepared in phosphate electrolytes. Electrochem. Commun. 7(5), 505–509 (2005)

    Article  Google Scholar 

  15. K. Shavanova, Y. Bakakina, I. Burkova, I. Shtepliuk et al., Application of 2D non-graphene materials and 2D oxide nanostructures for biosensing technology. Sensors 16(2), 223 (2016)

    Article  ADS  Google Scholar 

  16. C.A. Grimes, G.K. Mor, TiO2 nanotube arrays: Synthesis, properties, and applications (Springer, New York, 2009)

    Book  Google Scholar 

  17. M. Zhou, S. Roualdès, A. Ayral, New photocatalytic contactors obtained by PECVD deposition of \(TiO_2\) thin layers on the surface of macroporous supports. Eur. Phys. J.: Spec. Top. 224, 1871–1882 (2015)

    Google Scholar 

  18. S.A. Tomás, O. Zelaya, R. Palomino, R. Lozada, O. García, J.M. Yáñez, A. Ferreira da Silva, Optical characterization of sol gel \(TiO_2\) monoliths doped with brilliant green. Eur. Phys. J.: Spec. Top. 153, 255–258 (2008)

    Google Scholar 

  19. H.D. Jang, S.K. Kim, S.J. Kim, Effect of particle size and phase composition of titanium dioxide nanoparticles on the photocatalytic properties. J. Nanoparticle Res. 3(2), 141–147 (2001)

    Article  ADS  Google Scholar 

  20. O.K. Varghese, X. Yang, J. Kendig, M. Paulose, K. Zeng, C. Palmer, K. Ong, A transcutaneous hydrogen sensor: From design to application. Sens. Lett. 4(2), 120–128 (2006)

    Article  Google Scholar 

  21. S. Prabhu, M. Arulperumjothi, G. Murugan, V.M. Dhinesh, J.P. Kumar, On certain counting polynomial of titanium dioxide nanotubes. Nanosci. Nanotechnol. Asia. 9(2), 240–243 (2019)

    Article  Google Scholar 

  22. M. Arockiaraj, J.B. Liu, M. Arulperumjothi, S. Prabhu, On certain topological indices of three-layered single-walled titania nanosheets. Comb. Chem. High Throughput Screen. 25(3), 483–495 (2022)

    Article  Google Scholar 

  23. S. Mondal, M. Imran, N. De, A. Pal, Neighborhood M-polynomial of titanium compounds. Arab. J. Chem. 14(8), 103244 (2021)

    Article  Google Scholar 

  24. K. Wang, H. **, Q. Song, J. Huo, J. Zhang, P. Li, Titanium dioxide nanotubes as drug carriers for infection control and osteogenesis of bone implants. Drug Deliv. Transl. Res. 11(4), 1456–1474 (2021)

    Article  Google Scholar 

  25. S. Maher, A. Mazinani, M.R. Barati, D. Losic, Engineered titanium implants for localized drug delivery: Recent advances and perspectives of titania nanotubes arrays. Expert Opin. Drug Deliv. 15(10), 1021–1037 (2018)

    Article  Google Scholar 

  26. J. Park, A. Cimpean, A.B. Tesler, A. Mazare, Anodic \(TiO_2\) nanotubes: Tailoring osteoinduction via drug delivery. Nanomater. 11(9), 2359 (2021)

    Article  Google Scholar 

  27. L.X. Yang, S.L. Luo, Q.Y. Cai, S.Z. Yao, A review on \(TiO_2\) nanotube arrays: fabrication, properties, and sensing applications. Sci. Bull. 55(4), 331–338 (2010)

    Article  Google Scholar 

  28. S. Noreen, M.B. Tahir, A. Hussain, T. Nawaz et al., Emerging 2D-nanostructured materials for electrochemical and sensing application—A review. Int. J. Hydrog. Energy 47(2), 1371–1389 (2022)

    Article  Google Scholar 

  29. S. Sreekantan, K.A. Saharudin, L.C. Wei, Formation of \(TiO_2\) nanotubes via anodization and potential applications for photocatalysts, biomedical materials, and photoelectrochemical cell. IOP Conf. Ser.: Mater. Sci. Eng. 21, 012002 (2011)

    Article  Google Scholar 

  30. K. Indira, U.K. Mudali, T. Nishimura, N. Rajendran, A review on \(TiO_2\) nanotubes: Influence of anodization parameters, formation mechanism, properties, corrosion behavior, and biomedical applications. J. Bio. Tribo. Corros. 1(28), 1–22 (2015)

    Google Scholar 

  31. W.A. Abbas, I.H. Abdullah, B.A. Ali, N. Ahmed, A.M. Mohamed, M.Y. Rezk, N. Ismail, M.A. Mohamed, N.K. Allam, Recent advances in the use of \(TiO_2\) nanotube powder in biological, environmental, and energy applications. Nanoscale Adv. 1(8), 2801–2816 (2019)

    Article  ADS  Google Scholar 

  32. J. Bok, B. Furtula, N. Jedličková, R. Škrekovski, On extremal graphs of weighted Szeged index. MATCH Commun. Math. Comput. Chem. 82, 93–109 (2019)

    MATH  Google Scholar 

  33. N. Tratnik, Computing weighted Szeged and PI indices from quotient graphs. Int. J. Quantum Chem. 119(21), e26006 (2019)

    Article  Google Scholar 

  34. M. Arockiaraj, J. Clement, N. Tratnik, S. Mushtaq, K. Balasubramanian, Weighted Mostar indices as measures of molecular peripheral shapes with applications to graphene, graphyne and graphdiyne nanoribbons. SAR QSAR Environ. Res. 31(3), 187–208 (2020)

    Article  Google Scholar 

  35. I. Gutman, A formula for the Wiener number of trees and its extension to graphs containing cycles. Graph Theory Notes New York 27(9), 9–15 (1994)

    Google Scholar 

  36. A. Divya, A. Manimaran, Topological indices for the iterations of Sierpiński rhombus and Koch snowflake. Eur. Phys. J.: Spec. Top. 230, 3971–3980 (2021)

    Google Scholar 

  37. P.V. Khadikar, S. Karmarkar, V.K. Agrawal, A novel PI index and its applications to QSPR/QSAR Studies. J. Chem. Inf. Comput. Sci. 41(4), 934–949 (2001)

    Article  Google Scholar 

  38. I. Gutman, A.R. Ashrafi, The edge version of the Szeged index. Croat. Chem. Acta 81(2), 263–266 (2008)

    Google Scholar 

  39. M. Arockiaraj, S. Mushtaq, S. Klavžar, J.C. Fiona, K. Balasubramanian, Szeged-like topological indices and the efficacy of the cut method: The case of melem structures. Discr. Math. Lett. 9, 49–56 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  40. S. Brezovnik, N. Tratnik, General cut Method for computing Szeged-like topological indices with applications to molecular graphs. Int. J. Quantum Chem. 121(6), e26530 (2020)

    Google Scholar 

  41. M. Imran, M.A. Malik, R. Javed, On Szeged-type indices of titanium oxide \(TiO_2\) nanotubes. Int. J. Quantum Chem. 121(15), e26669 (2021)

    Article  Google Scholar 

  42. M. Arockiaraj, J. Clement, N. Tratnik, Mostar indices of carbon nanostructures and circumscribed donut benzenoid systems. Int. J. Quantum Chem. 119(24), e26043 (2019)

    Article  Google Scholar 

  43. T. Došlić, I. Martinjak, R. Škrekovski, S.T. Spužević, I. Zubac, Mostar index. J. Math. Chem. 56(10), 2995–3013 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  44. M. Arockiaraj, J. Clement, K. Balasubramanian, Topological indices and their applications to circumcised donut benzenoid systems, kekulenes and drugs. Polycycl. Aromat. Compd. 40(2), 280–303 (2020)

    Article  Google Scholar 

  45. M. Arockiaraj, S. Klavžar, S. Mushtaq, K. Balasubramanian, Distance-based topological indices of nanosheets, nanotubes and nanotori of \(SiO_2\). J. Math. Chem. 57, 343–369 (2018)

    Article  MATH  Google Scholar 

  46. M. Arockiaraj, J. Clement, K. Balasubramanian, Topological properties of carbon nanocones. Polycycl. Aromat. Compd. 40(5), 1332–1346 (2018)

    Article  Google Scholar 

  47. P.M. Winkler, Isometric embedding in products of complete graphs. Discr. Appl. Math. 7(2), 221–225 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  48. D.Ž Djoković, Distance-preserving subgraphs of hypercubes. J. Comb. Theory. Ser. B. 14(3), 263–267 (1973)

    Article  MathSciNet  Google Scholar 

  49. S. Nandi, M.C. Bagchi, QSAR of aminopyrido[2,3-d]pyrimidin-7-yl derivatives: Anticancer drug design by computed descriptors. J. Enzyme Inhib. Med. Chem. 24, 937–948 (2009)

    Article  Google Scholar 

  50. A. Thakur, M. Thakur, N. Kakani, A. Joshi et al., Application of topological and physicochemical descriptors: QSAR study of phenylamino-acridine derivatives. ARKIVOC 2004(14), 36–43 (2004)

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank Vellore Institute of Technology, Vellore for providing ‘VIT SEED Grant-RGEMS Fund (SG20220048)’ for carrying out this research work.

Author information

Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India

    J. Singh Junias & Joseph Clement

Authors
  1. J. Singh Junias
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Joseph Clement
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Joseph Clement.

Additional information

Recent Advancements in Composite Materials and Structures for Energy applications. Guest editor: Nuggehalli M. Ravindra.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Singh Junias, J., Clement, J. Weighted bond-additive descriptors of titanium oxide nanosheet. Eur. Phys. J. Spec. Top. (2023). https://doi.org/10.1140/epjs/s11734-023-00807-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjs/s11734-023-00807-7

Search

Navigation