Inverse and Hyper Zagreb Indices: Application to Quantitative Structure Properties Relationship

  • Ahmad Nazib Alias Dr

Abstract

The topology index can be derived from molecular connectivity, which can be related to the chemical or physical properties of molecules. The topology indices of alkanes are calculated using the modified-Zagreb index, direct and reciprocal degree distance indices, and the modified-Zagreb index. These indices are tested as the structural descriptor for thermodynamic properties such as boiling point (bp), heat vaporization at 25oC (hv), critical temperature (ct), critical pressure (PC) and magnetooptical properties. Multiple linear regression analyses were done to find the best fitting between these indices and the thermodynamic properties. The results indicate that the boiling point, critical temperature, and heat vapor are reasonably well accounted for by the presence of more than two parameters. The regression equation for the four thermodynamic properties and magnetooptical properties shows a good relation property.

References

[1] M. Takata, B.-L. Lin, M. Xue, Y. Zushi, A. Terada, and M. Hosomi, "Predicting the acute ecotoxicity of chemical substances by machine learning using graph theory," Chemosphere, vol. 238, p. 124604, 2020.
[2] E. A. Walker, M. M. Mohammadi, and M. T. Swihart, "Graph Theory Model of Dry Reforming of Methane Using Rh(111)," The Journal of Physical Chemistry Letters, vol. 11, no. 12, pp. 4917-4922, 2020.
[3] I. Gutman and N. Trinajstić, "Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons," Chemical Physics Letters, vol. 17, no. 4, pp. 535-538, 1972.
[4] A. Ali and N. Trinajstić, "A Novel/Old Modification of the First Zagreb Index," Molecular Informatic vol. 37, no. 6-7, p. 1800008, 2018.
[5] M. Alsharafi, M. Shubatah, and A. Alameri, "The hyper-Zagreb index of some complement graphs," Advances in Mathematics: Scientific Journal, vol. 9, no. 6, pp. 3631-3642, 2020.
[6] K. Al-Malah, "Prediction of Critical Temperature and Pressure of Hydrocarbons Using Simple Molecular Properties," Advanced Aspects of Engineering Research, vol. 10, pp. 130-148, 2021.
[7] J. Cao, U. Ali, M. Javaid, and C. Huang, "Zagreb Connection Indices of Molecular Graphs Based on Operations," Complexity, vol. 2020, p. 7385682, 2020.
[8] Y.-M. Chu, K. Julietraja, P. Venugopal, M. K. Siddiqui, and S. Prabhu, "Degree- and irregularity-based molecular descriptors for benzenoid systems," The European Physical Journal Plus, vol. 136, no. 1, p. 78, 2021.
[9] K. A. Kumar, N. Basavarajappa, and Shanmukha, "QSPR analysis of Alkanes with certain degree based topological indices," Malaya Journal of Matematik, vol. 8, no. 2, 2020, pp. 314-330, 2020.
[10] D. Zhao, M. K. Siddiqui, I. Z. Cheema, M. H. Muhammad, A. Rauf, and M. Ishtiaq, "On Molecular Descriptors of Polycyclic Aromatic Hydrocarbon," Polycyclic Aromatic Compounds, pp. 1-12, 2020.
[11] W. N. N. N. W. Zuki, Z. Du, M. Kamran Jamil, and R. Hasni, "Extremal Trees with Respect to the Difference between Atom-Bond Connectivity Index and Randić Index," Symmetry vol. 12, no. 10, p. 1591, 2020.
[12] I. Gutman, "Relation between geometric–arithmetic and arithmetic–geometric indices," Journal of Mathematical Chemistry, vol. 59, no. 6, pp. 1520-1525, 2021.
[13] Monika Singh, Harish Dureja, and A. K. Madan, "Randic Index and Its Variants: Applications," in New Frontiers in Nanochemistry, M. V. Putz, Ed. Boca Raton: Apple Academic Press, 2020.
[14] A. Alqesmah, K. A. A. Alloush, A. Saleh, and G. Deepak, "Entire Harary index of graphs," Journal of Discrete Mathematical Sciences and Cryptography, pp. 1-15, 2021.
[15] F. Safa and M. Jafari Ghadimi, "Graph Theoretical Atom-Type-Based Descriptors for Structural Characterization and Retention Prediction of Acyclic Alkanes," Moscow University Chemistry Bulletin, vol. 76, no. 2, pp. 157-168, 2021.
[16] A. A. Toropov and A. P. Toropova, "QSPR/QSAR: State-of-Art, Weirdness, the Future," Molecules, vol. 25, no. 6, p. 1292, 2020.
[17] B. Horoldagva and K. C. Das, "On Zagreb indices of graphs," MATCH Commun. Math. Comput. Chem, vol. 85, pp. 295-301, 2021.
[18] S. Gumus and L. Turker, "TG index and its application on alkanes and alkenes," Chemistry Journal, vol. 1, pp. 103-115, 2015.
Published
2021-11-02
How to Cite
ALIAS, Ahmad Nazib. Inverse and Hyper Zagreb Indices: Application to Quantitative Structure Properties Relationship. Mathematical Sciences and Informatics Journal, [S.l.], p. 44-50, nov. 2021. ISSN 2735-0703. Available at: <https://myjms.mohe.gov.my/index.php/mij/article/view/13970>. Date accessed: 07 dec. 2022. doi: https://doi.org/10.24191/mij.v2i2.13970.
Section
Articles

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