Skip to main content
SpringerLink
Log in

Characterizing superlattice topologies via fifth M-Zagreb polynomials and structural indices

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

Abstract

Graph theory provides a strong framework for evaluating and comprehending atom and molecule connections and interactions. Chemical compounds are represented as graphs with edges and vertices. Topological indices have a wide range of applications in the world of research. Topological indices are used for the prediction of chemical compound's properties (boiling point, strain energy, distortion, and stability). The calculation of various indices and polynomials for a molecular graph of a super lattice demonstrates the utilization of graph theory. In the characterization and analysis of molecular structures, including based on degrees, fifth M-Zagreb indices, fifth hyper-M-Zagreb indices, fifth \(M_{2}\)-Zagreb polynomials, fifth \(M_{1}\)-Zagreb polynomials, and fifth \(M_{1}\)-Zagreb polynomials in general.

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

Access this article

Log in via an institution

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

Similar content being viewed by others

Data availability

In this article, no data were utilized.

References

  1. A. Al Khabyah, Mathematical aspects and topological properties of two chemical networks. AIMS Mathematics 8(2), 4666–4681 (2023)

    Article  MathSciNet  Google Scholar 

  2. H. Ali, M.A. Binyamin, M.K. Shafiq, W. Gao, On the degree-based topological indices of some derived networks. Mathematics 7(7), 6–12 (2019)

    Article  Google Scholar 

  3. A. Ali, M. Zahid, W. Gao, M. Imran, Topological indices and cheminformatics applications. Mol. Sci. 22(6), 30–96 (2021)

    Google Scholar 

  4. D. Amic, D. Beslo, B. Lucic, S. Nikolic, N. Trinajstic, The vertex-connectivity index revisited. J. Chem. Inf. Comput. Sci. 38(5), 819–822 (1998)

    Article  Google Scholar 

  5. M. Ali, A. Latif, S. Gao, K. Mahmood, QSPR modeling of boiling point of organic compounds using topological indices. Mol. Liq. 279, 177–184 (2019)

    Google Scholar 

  6. M. Eliasi, A. Iranmanesh, I. Gutman, Multiplicative versions of first Zagreb index. Match-Commun. Math. Comput. Chem. 68(1), 2–17 (2012)

    MathSciNet  MATH  Google Scholar 

  7. B. Furtula, A. Graovac, Novel vertex-weighted molecular topological indices. J. Comput. Chem. 32(12), 2726–2739 (2011)

    Google Scholar 

  8. I. Gutman, N. Trinajstic, Graph theory and molecular orbitals. Total f-electron energy of alternant hydrocarbons. Chem. Phys. Lett. 17(4), 535–538 (1972)

    Article  ADS  Google Scholar 

  9. Xiujun Zhang, Hafiz Muhammad Awais, Muhammad Javaid, Muhammad Kamran Siddiqui, Multiplicative Zagreb indices of molecular graphs. J. Chem. 2019, 1–19 (2019)

    Article  Google Scholar 

  10. X. Zhang, H. Jiang, J.B. Liu, Z. Shao, The cartesian product and join graphs on edge-version atom-bond connectivity and geometric arithmetic indices. Molecules 23(7), 17–31 (2018)

    Article  Google Scholar 

  11. Z. Shao, M.K. Siddiqui, M.H. Muhammad, Computing Zagreb indices and Zagreb polynomials for symmetrical nanotubes. Symmetry 10(7), 244–260 (2018)

    Article  ADS  Google Scholar 

  12. W. Gao, M.K. Siddiqui, M. Naeem, N.A. Rehman, Topological characterization of carbon graphite and crystal cubic carbon structures. Molecules 22(9), 1496–1515 (2017)

    Article  Google Scholar 

  13. X. Zhang, A. Rauf, M. Ishtiaq, M.K. Siddiqui, M.H. Muhammad, On degree based topological properties of two carbon nanotubes. Polycyclic Aromat. Compd. 42(3), 866–884 (2022)

    Article  Google Scholar 

  14. X. Zhang, M. Naeem, A.Q. Baig, M.A. Zahid, Study of hardness of superhard crystals by topological indices. J. Chem. 2021, 1–10 (2021)

    Google Scholar 

  15. X. Zhang, M.K. Siddiqui, S. Javed, L. Sherin, F. Kausar, M.H. Muhammad, Physical analysis of heat for formation and entropy of Ceria Oxide using topological indices. Combinatorial Chem. High Throughput Screen. 25(3), 441–450 (2022)

    Article  Google Scholar 

  16. X. Zhang, Z. Zhang, N. Chidambaram, S. Jaganathan, N. Devadoss, V. Ravi, On degree and distance-based topological indices of certain interconnection networks. Eur. Phys. J. Plus 137(7), 1–15 (2022)

    Article  Google Scholar 

  17. I. Gutman, Degree-based topological indices. Croat. Chem. Acta 86(4), 351–361 (2013)

    Article  Google Scholar 

  18. I. Gutman, N. Trinajstic, Graph theory and molecular orbitals. XIII. On the stability of annelated tropylium cations. Croat. Chem. Acta 46(4), 243–248 (1974)

    Google Scholar 

  19. I. Gutman, Multiplicative Zagreb indices of trees. Bull. Soc. Math. Banja Luka 18, 17–23 (2011)

    MATH  Google Scholar 

  20. M. Ghorbani, A.R. Ashrafi, S.R. Pour, Some new degree-based topological indices. Comput. Chem. 39(28), 2444–2455 (2018)

    Google Scholar 

  21. A. Graovac, M. Ghorbani, M.A. Hosseinzadeh, Computing fifth geometric-arithmetic index for nanostar dendrimers. J. Discret. Math. Appl. 1(1–2), 33–42 (2011)

    Google Scholar 

  22. R. Huang, M.H. Muhammad, M.K. Siddiqui, S. Khalid, S. Manzoor, E. Bashier, Analysis of topological aspects for metal-insulator transition superlattice network. Complexity 10, 1–12 (2022)

    Google Scholar 

  23. V.R. Kulli, Multiplicative hyper-Zagreb indices and coindices of graphs: computing these indices of some nanostructures. Int. Res. J. Pure Algebra 6(7), 342–347 (2016)

    Google Scholar 

  24. V.R. Kulli, General fifth M-Zagreb indices and fifth M-Zagreb polynomials of PAMAM dendrimers. Int. J. Fuzzy Math. Arch. 13(1), 99–103 (2017)

    Article  Google Scholar 

  25. V.R. Kulli, B. Chaluvaraju, T.V. Asha, Multiplicative product connectivity and sum connectivity indices of chemical structures in drugs. Res. Rev. Int. J. Multidiscip. 4(2), 949–953 (2019)

    Google Scholar 

  26. V.R. Kulli, HDR Zagreb indices of remdesivir, chloroquine, hydroxychloroquine: research for the treatment of COVID-19. SSRG Int. J. Appl. Chem. 9(1), 1–9 (2022)

    Article  MathSciNet  Google Scholar 

  27. W. Liu, Z. Zhu, K. Cai, D. Pu, Y. Du, Application of knowledge graph in smart grid fault diagnosis. Appl. Math. Nonlinear Sci. (2022)

  28. J. Lu, L. Zhu, W. Gao, Remarks on bipolar cubic fuzzy graphs and its chemical applications. Int. J. Math. Comput. Eng. 1(1), 1–10 (2023)

    Article  Google Scholar 

  29. L. Ma, C. Dou, T. Hao, Grid data asset relationship and intelligent classification integrating knowledge graph and Internet of Things. Appl. Math. Nonlinear Sci. 24(5), 328–340

  30. S. Nagarajan, M. Imran, P.M. Kumar, K. Pattabiraman, M.U. Ghani, Degree-based entropy of some classes of networks. Mathematics 11(4), 960–967 (2023)

    Article  Google Scholar 

  31. S. Raoux, W. Welnic, D. Ielmini, Phase change materials and their application to nonvolatile memories. Chem. Rev. 110(1), 240–267 (2010)

    Article  Google Scholar 

  32. V.K. Sharma, S. Sharma, A.K. Madan, A review on distance-based topological indices in quantitative structure activity relationship. Comput. Chem. 40(8), 839–876 (2019)

    Google Scholar 

  33. R.E. Simpson, P. Fons, A.V. Kolobov, T. Fukaya, M. Krbal, S. Yagi, Disorder-order phase transition in GeSbTe. Appl. Phys. 109(10), 1024–1040 (2011)

    Google Scholar 

  34. Y. Wu, F. Lv, M. Li, The application of graph theory teaching method in ideological and political education of discrete mathematics. Appl. Math. Nonlinear Sci. 39(6), 8125–8137

Download references

Funding

This research received no funding.

Author information

Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan

    Hani Shaker & Muhammad Kamran Siddiqui

  2. Department of Mathematics, Government College University, Lahore, Pakistan

    Sabeen Javaid, Usman Babar & Asim Naseem

Authors
  1. Hani Shaker
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sabeen Javaid
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Usman Babar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Muhammad Kamran Siddiqui
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Asim Naseem
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Kamran Siddiqui.

Ethics declarations

Conflict of interest

Authors have no conflict of interest.

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

Shaker, H., Javaid, S., Babar, U. et al. Characterizing superlattice topologies via fifth M-Zagreb polynomials and structural indices. Eur. Phys. J. Plus 138, 1025 (2023). https://doi.org/10.1140/epjp/s13360-023-04645-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-023-04645-3

Search

Navigation