Modelling Physico-Chemical Properties of Benzenes Via Zagreb Tau Indices

Abstract

Quantitative structure-property relationship (QSPR) studies use topological indices to explain the chemical and physical properties of molecular entities. In this study, we primarily determined the tau degree of a vertex along with the Zagreb tau indices for connected graphs, which represents a significant advancement in the field of (chemical) graph theory. It has been shown that there are correlations exceeding 0.95 between Zagreb tau indices and the physicochemical properties of benzenes, including boiling point, pi-electron energy, molecular weight, polarization, molecular volume, and relative formula mass. The findings show that the correlation coefficients between Zagreb tau indices and the degree-based topological indices of benzenes exceed 0.92. Additionally, structural sensitivity and abrupt change analyses were conducted on these new indices, and they were compared with other topological indices. The results and analyses confirm that the Zagreb tau indices are applicable in QSPR research efforts.

Keywords

• QSPR studies
• Benzenes
• Topological indices
• Tau degree
• Zagreb tau indices

References

1. [1]. H. Wiener, Structural determination of paraffin boiling points, J. Am. Chem. Soc. 69 (1947), 17–20.
2. [2]. J. R. Platt, Influence of neighbour bonds on additive bond properties in paraffins, J. Chem. Phys. 15 (1947) 419-420.
3. [3]. V. Kumar, S. Das, On Structure Sensitivity and Chemical Applicability of Some Novel Degree-Based Topological Indices, MATCH Commun. Math. Comput. Chem. 92 (2024) 165–203.
4. [4]. I. Gutman, N. Trinajstić, Graph theory and molecular orbitals, Total π electron energy of alternant hydrocarbons, Chem. Phys. Lett. 17 (1972) 535–538.
5. [5]. M. Randić, Characterization of molecular branching, J. Am. Chem. Soc. 97 (1975) 6609–6615.
6. [6]. I. Gutman, B. Furtula, C. Elphick, Three new/old vertex-degree-based topological indices, MATCH Commun. Math. Comput. Chem.72 (2014) 617–632.
7. [7]. B. Zhou, N. Trinajstić, On a novel connectivity index, J. Math. Chem. 46 (2009) 1252–1270.
8. [8]. D. Vukičević, M. Gašperov, Bond additive modeling 1. Adriatic indices, Croat. Chem. Acta 83 (2010) 243–260.

9. [9]. O. Favaron, M. Mahéo, J. F. Saclé, Some eigenvalue properties in graphs (conjectures of graffiti-II), Discrete Math. 111 (1993) 197–220.
10. [10]. E. Estrada, L. Torres, L. Rodriguez, I. Gutman, An atom-bond connectivity index: modelling the enthalpy of formation of alkanes, Indian J. Chem. 37A (1998) 849–855.
11. [11]. B. Furtula, A. Graovac, D. Vukičević, Augmented Zagreb index, J. Math. Chem. 48 (2010) 370–380.
12. [12]. G. Shirdel, H. Rezapour, A. Sayadi, The hyper-Zagreb index of graph operations, Iran. J. Math. Chem. 4 (2013) 213–220.
13. [13]. A. Alameri, Second hyper-Zagreb index of titania nanotubes and their applications, IEEE Access. 9 (2021) 9567–9571.
14. [14]. D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46 (2009) 1369–1376.
15. [15]. S. Ediz, Computing GA4 index of an infinite class of nanostar dendrimers, Optoelectronics and Advanced Materials Rapid Communications 4 (12) (2010) 2198-2199.
16. [16]. V. Shegehalli, R. Kanabur, Arithmetic-Geometric indices of path graph, J. Comput. Math. Sci. 16 (2015) 19–24.
17. [17]. I. Gutman, Geometric approach to degree-based topological indices:Sombor indices, MATCH Commun. Math. Comput. Chem. 86 (2021)11–16.
18. [18]. V. Kulli, I. Gutman, Computation of Sombor indices of certain networks, SSRG Int. J. Appl. Chem. 8 (2021) 1–5.
19. [19]. V. Kulli, Nirmala index, Int. J. Math. Trends Technol. 67 (2021)8–12.
20. [20]. V. Kulli, V. Lokesha, K. Nirupadi, Computation of inverse Nirmala indices of certain nanostructures, Int. J. Math. Comb. 2 (2021) 33–40.
21. [21]. S. Nikolić, N. Trinajstić, Comparison between the Vertex- and Edge-Connectivity Indices for Benzenoid Hydrocarbons, J. Chem. Inf. Comput. Sci. 38 (1998) 42-46
22. [22]. S. Hayat, S. Khan, A. Khan, M. Imran, Distance-based topological descriptors for measuring the 𝜋-electronic energy of benzenoid hydrocarbons with applications to carbon nanotubes, Math Meth Appl Sci. (2020) 1–20.
23. [23]. S. Hayat, S. Khani, A. Khan, M. Imran, A Computer-Based Method to Determine Predictive Potential of Distance-Spectral Descriptors for Measuring the π-Electronic Energy of Benzenoid Hydrocarbons with Applications, IEEE Access 9 (2021) 19238-19253.
24. [24]. M. C. Shanmukha, A. Usha, V. R. Kulli, K. C. Shilpa, Chemical applicability and curvilinear regression models of vertex-degree-based topological index: Elliptic Sombor index, Int J Quantum Chem. 2024;124: e27376.
25. [25]. M. Y. H. Malik, M. A. Binyamin, S. Hayat, Correlation ability of degree-based topological indices for physicochemical properties of polycyclic aromatic hydrocarbons with applications, Polycyclic Aromatic Compounds 42 (2022) 6267-6281.
26. [26]. B. Furtula, I. Gutman, M. Dehmer, On structure-sensitivity of degree-based topological indices, Appl. Math. Comput. 219 (2013) 8973–8978.
27. [27]. I. Redžepović, B. Furtula, Comparative study on structural sensitivity of eigenvalue-based molecular descriptors, J. Math. Chem. 59 (2021) 476–487.
28. [28]. K. Zemljič, P. Žigert Pleteršek, Smoothness of graph energy in chemical graphs, Mathematics 11 (2023) #552.
29. [29] H. Hosoya, The most private features of the topological index, MATI (1) (2019), 25-33