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On Nirmala Indices-based Entropy Measures of Silicon Carbide Network \(Si_{2}C_{3}-III[\alpha ,\beta ]\)

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Abstract

A numerical parameter, referred to as a topological index, is used for representing the molecular structure of a compound by analyzing its graph-theoretical characteristics. In the context of quantitative structure-activity relationship (QSAR) and quantitative structure-property relationship (QSPR) studies, topological indices serve as predictive tools for the physicochemical properties of chemical compounds. Graph entropies have evolved into information-theoretic instruments for exploring the structural information of molecular graphs. In this research, we compute the Nirmala index, as well as the first and second inverse Nirmala index, for the silicon carbide network \(Si_{2}C_{3}-III[\alpha ,\beta ]\), using its M-polynomial. The comparison of the Nirmala indices and corresponding entropy measures are presented through numerical computation and 2D line plots. A regression model is built to investigate the relationship between the Nirmala indices and corresponding entropy measures.

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References

  1. Wagner S, Wang H (2019) Introduction to Chemical Graph Theory, Discrete Mathematics and its Applications. CRC Press, Boca Raton

    Google Scholar 

  2. Trinajstic N (2018) Chemical Graph Theory. CRC Press, Boca Raton

    Book  Google Scholar 

  3. Das S, Rai S, Kumar V (2023) On topological indices of Molnupiravir and its QSPR modeling with some other antiviral drugs to treat COVID-19 patients. J. Math. Chem. 1-44

  4. Deng H, Yang J, **a F (2011) A general modeling of some vertex-degree based topological indices in benzenoid systems and phenylenes. Comput. Math. with Appl. 61:3017–3023

    Article  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  6. Randić M (1975) Characterization of molecular branching. J Am Chem Soc 97:6609–6615

    Article  Google Scholar 

  7. Gutman I, Trinajstić N (1972) Graph theory and molecular orbitals. Total \(\pi \)-electron energy of alternant hydrocarbons. Chem Phys Lett 17:535–538

    Article  CAS  Google Scholar 

  8. Das S, Rai S, Mandal M (2023) M-polynomial and correlated topological indices of antiviral drug Molnupiravir used as a therapy for COVID-19. Polycycl Aromat Compd 43:7027–7041

    Article  CAS  Google Scholar 

  9. Kulli VR (2021) Nirmala index. Int. J. Math. Trends Technol. 67:8–12

    Article  Google Scholar 

  10. Kulli VR, Lokesha V, Nirupadi K (2021) Computation of inverse Nirmala indices of certain nanostructures. International J. Math. Combin. 2:33–40

    Google Scholar 

  11. Hosoya H (1988) On some counting polynomials in chemistry. Discrete Appl. Math. 19:239–257

    Article  Google Scholar 

  12. Verma A, Mondal S, De N, Pal A (2019) Topological properties of bismuth tri-iodide using neighborhood M-polynomial. Int. J. Math. Trends Technol. 67:83–90

    Article  Google Scholar 

  13. Deutsch E, Klavžar S (2015) M-polynomial and degree-based topological indices. Iran. J. Math. Chem. 6:93–102

    Google Scholar 

  14. Kwun YC, Munir M, Nazeer W, Rafique S, Kang SM (2017) M-polynomials and topological indices of V-Phenylenic nanotubes and nanotori. Sci Rep 7:8756

    Article  PubMed  PubMed Central  Google Scholar 

  15. Munir M, Nazeer W, Rafique S, Kang SM (2016) M-polynomial and related topological indices of nanostar dendrimers. Symmetry 8:97

    Article  Google Scholar 

  16. Das S, Rai S (2020) M-polynomial and related degree-based topological indices of the third type of Hex-derived network. Nanosyst. Phys. Chem. Math. 11:267–274

    Article  Google Scholar 

  17. Das S, Rai S (2020) M-polynomial and related degree-based topological indices of the third type of chain Hex-derived network. Malaya J. Mat. 8:1842–1850

    Article  Google Scholar 

  18. Das S, Kumar V (2022) On M-polynomial of the two-dimensional silicon-carbons. Palest. J. Math. 11:136–157

    Google Scholar 

  19. Das S, Kumar V (2022) Investigation of closed derivation formulas for GQ and QG indices of a graph via M-polynomial. Iran. J. Math. Chem. 13:129–144

  20. Das S, Rai S (2023) On closed derivation formulas of Nirmala indices from the M-polynomial of a graph. J Indian Chem Soc 100:101017

    Article  CAS  Google Scholar 

  21. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423

    Article  Google Scholar 

  22. Huang R, Siddiqui MK, Manzoor S, Khalid S, Almotairi S (2022) On physical analysis of topological indices via curve fitting for the natural polymer of cellulose network. Eur. Phys. J. Plus 137:1–17

    Article  Google Scholar 

  23. Wang XL, Siddiqui MK, Kirmani SAK, Manzoor S, Ahmad S, Dhlamini M (2021) On topological analysis of entropy measures for silicon carbides networks. Complexity 2021:1–26

    Google Scholar 

  24. Manzoor S, Siddiqui MK, Ahmad S (2022) On entropy measures of polycyclic hydroxy-chloroquine used for novel coronavirus (COVID-19) treatment. Polycycl Aromat Compd 42:2947–2969

    Article  CAS  Google Scholar 

  25. Manzoor S, Siddiqui MK, Ahmad S (2020) On entropy measures of molecular graphs using topological indices. Arab J Chem 13:6285–6298

    Article  CAS  Google Scholar 

  26. Hayat S (2024) Seham J F Alanazi and Jia-Bao Liu, Two novel temperature-based topological indices with strong potential to predict physicochemical properties of polycyclic aromatic hydrocarbons with applications to silicon carbide nanotubes. Phys Scr 99:055027

    Article  Google Scholar 

  27. Hayat S, Mahadi H, Alanazi SJF, Wang S (2024) Predictive potential of eigenvalues-based graphical indices for determining thermodynamic properties of polycyclic aromatic hydrocarbons with applications to polyacenes. Comput Mater Sci 238:112944

    Article  CAS  Google Scholar 

  28. Hayat S, Liu J-B (2024) Comparative analysis of temperature-based graphical indices for correlating the total \(\pi \)-electron energy of benzenoid hydrocarbons. J Mod Phys B. https://doi.org/10.1142/s021797922550047x

    Article  Google Scholar 

  29. Hayat S, Khan A, Ali K, Liu J-B (2024) Structure-property modeling for thermodynamic properties of benzenoid hydrocarbons by temperature-based topological indices. Ain Shams Engineering Journal. 15:102586

    Article  Google Scholar 

  30. Hayat S (2023) Distance-based graphical indices for predicting thermodynamic properties of benzenoid hydrocarbons with applications. Comput Mater Sci 230:112492

    Article  CAS  Google Scholar 

  31. Hayat S, Suhaili N, Jamil H (2023) Statistical significance of valency-based topological descriptors for correlating thermodynamic properties of benzenoid hydrocarbons with applications. Comput Theor Chem 1227:114259

    Article  CAS  Google Scholar 

  32. Chen Z, Dehmer M, Shi Y (2014) A note on distance-based graph entropies. Entropy 16:5416–5427

    Article  Google Scholar 

  33. Kumar V, Das S (2023) On Nirmala Indices-based Entropy Measures of Silicon Carbide Network. Iran. J. Math. Chem. 14:271–288

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, School of Applied Sciences, REVA University, Kattigenahalli, Bangalore, 560064, Karnataka, India

    H. C Shilpa & K Gayathri

  2. Post Graduate Department of Mathematics, Maharani’s Science College for Women, Mysore, 570005, Karnataka, India

    B. N. Dharmendra

  3. Department of Science and Humanities, PES University, Bangalore, Karnataka, India

    H. M Nagesh

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

    Muhammad Kamran Siddiqui

Authors
  1. H. C Shilpa
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  2. K Gayathri
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  3. B. N. Dharmendra
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  4. H. M Nagesh
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  5. Muhammad Kamran Siddiqui
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All authors have contributed equally to the work done in the paper.

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Correspondence to H. C Shilpa.

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Shilpa, H.C., Gayathri, K., Dharmendra, B.N. et al. On Nirmala Indices-based Entropy Measures of Silicon Carbide Network \(Si_{2}C_{3}-III[\alpha ,\beta ]\). Silicon (2024). https://doi.org/10.1007/s12633-024-03071-z

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