Startseite Topological descriptors and connectivity analysis of coronene fractal structures: insights from atom-bond sum-connectivity and Sombor indices
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Topological descriptors and connectivity analysis of coronene fractal structures: insights from atom-bond sum-connectivity and Sombor indices

  • Xiujun Zhang , Sahar Aftab , Sadia Noureen EMAIL logo , Adnan Aslam ORCID logo und Sobhy M. Ibrahim
Veröffentlicht/Copyright: 10. Februar 2025
Zeitschrift für Naturforschung A
Aus der Zeitschrift Zeitschrift für Naturforschung A Band 80 Heft 3

Abstract

Coronene, a polycyclic aromatic hydrocarbon (PAH) consisting of six benzene rings fused in a hexagonal arrangement, exhibits a fractal structure that is significant in various fields such as condensed matter physics, materials science, surface science, and interdisciplinary areas like nanotechnology and astrochemistry. Topological descriptors, which characterize the geometric and connectivity properties of a structure independently of specific spatial coordinates, are crucial for understanding coronene’s complex geometry and connectivity. In this study, we compute the atom-bond sum (ABS)-connectivity index and four versions of the Sombor indices for three different configurations of the coronene fractal structure: Zig-zag Hexagonal Coronene Fractal (ZHCF), Armchair Hexagonal Coronene Fractal (AHCF), and Rectangular Coronene Fractal (RCF). To assess their chemical applicability, we develop linear regression models to estimate the physicochemical properties boiling point (BP) and molecular weight (MW) of benzene derivatives using these topological indices. The regression parameters for each case are provided, and the results show that the ABS index outperforms all other topological indices, making it the most effective predictor for these properties.

Keywords: topological index; chemical graph theory; ABS-index and invariants of Sombor index; coronene fractals
Corresponding author: Sadia Noureen, Department of Mathematics, Faculty of Science, University of Gujrat, Gujrat, Pakistan, E-mail:

Funding source: This work was supported by Researchers Supporting Project number (RSP2025R100), King Saud University, Riyadh, Saudi Arabia.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission. All authors contributed equally.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors state no conflict of interest.

  6. Research funding: This work was supported by Researchers Supporting Project number (RSP2025R100), King Saud University, Riyadh, Saudi Arabia.

  7. Data availability: Not applicable.

References

[1] K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons, 2004.10.1002/0470013850Suche in Google Scholar

[2] J. E. Hutchinson, “Fractals and self similarity,” Ind. Univ. Math. J., vol. 30, no. 5, pp. 713–747, 1981. https://doi.org/10.1512/iumj.1981.30.30055.Suche in Google Scholar

[3] M. Arockiaraj, J. Jency, J. Abraham, S. Ruth Julie Kavitha, and K. Balasubramanian, “Two-dimensional coronene fractal structures: topological entropy measures, energetics, NMR and ESR spectroscopic patterns and existence of isentropic structures,” Mol. Phys., vol. 120, no. 11, p. e2079568, 2022. https://doi.org/10.1080/00268976.2022.2079568.Suche in Google Scholar

[4] J.-B. Liu, X. Zhang, and J. Cao, “Structural properties of extended pseudo-fractal scale-free network with higher network efficiency,” J. Complex Netw., vol. 3, no. 3, pp. 1–16, 2024. https://doi.org/10.1093/comnet/cnae023.Suche in Google Scholar

[5] M. Bernkopf, “A history of infinite matrices: a study of denumerably infinite linear systems as the first step in the history of operators defined on function spaces,” Arch. Hist. Exact Sci., vol. 4, no. 4, pp. 308–358, 1968. https://doi.org/10.1007/bf00411592.Suche in Google Scholar

[6] S. K. Pandey and M. Yadav, “Fractint formula for overlaying fractals,” J. Inf. Syst. Commun., vol. 3, no. 1, p. 347, 2012.Suche in Google Scholar

[7] F. Dyson, “Characterizing irregularity: fractals. Form, chance, and dimension. Benoit B. Mandelbrot. Translation and revision of French edition (Paris, 1975). Freeman, San Francisco, 1977. Xviii, 366 pp., illus. 14.95,” Science, vol. 200, no. 4342, pp. 677–678, 1978. https://doi.org/10.1126/science.200.4342.677.Suche in Google Scholar PubMed

[8] B. B. Mandelbrot, C. J. Evertsz, and M. C. Gutzwiller, Fractals and Chaos: The Mandelbrot Set and Beyond, vol. 3, New York, Springer, 2004.10.1007/978-1-4757-4017-2Suche in Google Scholar

[9] D. Delignières, M. Fortes, and G. Ninot, “The fractal dynamics of self-esteem and physical self,” Nonlinear Dyn. Psychol. Life Sci., vol. 8, no. 4, pp. 479–510, 2004.Suche in Google Scholar

[10] A. L. Goldberger and D. R. Rigney, “On the non-linear motions of the heart: fractals, chaos and cardiac dynamics,” in Cell to Cell Signalling, Academic Press, 1989, pp. 541–550.10.1016/B978-0-12-287960-9.50045-9Suche in Google Scholar

[11] S. Havlin, et al.., “Fractals in biology and medicine,” Chaos, Solit. Fractals, vol. 6, pp. 171–201, 1995, https://doi.org/10.1016/0960-0779(95)80025-c.Suche in Google Scholar PubMed

[12] J.-B. Liu, L. Guan, and J. Cao, “Property analysis and coherence dynamics for tree-symmetric networks with noise disturbance,” J. Complex Netw., vol. 12, no. 4, p. cnae029, 2024. https://doi.org/10.1093/comnet/cnae029.Suche in Google Scholar

[13] J. Odom and T. Wood, “Exploration of the Sierpinski triangle with GeoGebra,” N. Am. GeoGebra J., vol. 6, no. 1, 2017.Suche in Google Scholar

[14] E. Pearse, “An introduction to dimension theory and fractal geometry: fractal dimensions and measures,” 2005. Available at: http://pi.math.cornell.edu/erin/docs/dimension.pdf.Suche in Google Scholar

[15] J. W. Baish and R. K. Jain, “Fractals and cancer,” Cancer Res., vol. 60, no. 14, pp. 3683–3688, 2000.Suche in Google Scholar

[16] K. J. Gowtham and I. V. A. N. Gutman, “On the difference between atom-bond sum-connectivity and sum-connectivity indices,” Bull. Cl. Sci. Math. Nat. Sci. Math., vol. 47, pp. 55–65, 2022.Suche in Google Scholar

[17] J. A. Bondy and U. S. R. Murty, Graph Theory with Applications, Ontario, Macmillan, 1976.10.1007/978-1-349-03521-2Suche in Google Scholar

[18] A. Ahmad, K. Elahi, R. Hasni, and M. F. Nadeem, “Computing the degree based topological indices of line graph of benzene ring embedded in P-type-surface in 2D network,” J. Inf. Optim. Sci., vol. 40, no. 7, pp. 1511–1528, 2019. https://doi.org/10.1080/02522667.2018.1552411.Suche in Google Scholar

[19] R. Huang, M. F. Hanif, M. K. Siddiqui, M. F. Hanif, and F. B. Petros, “Analyzing boron oxide networks through Shannon entropy and Pearson correlation coefficient,” Sci. Rep., vol. 14, no. 1, p. 26552, 2024. https://doi.org/10.1038/s41598-024-77838-0.Suche in Google Scholar PubMed PubMed Central

[20] S. C. Basak, V. R. Magnuson, G. J. Niemi, R. R. Regal, and G. D. Veith, “Topological indices: their nature, mutual relatedness, and applications,” Math. Model., vol. 8, pp. 300–305, 1987, https://doi.org/10.1016/0270-0255(87)90594-x.Suche in Google Scholar

[21] M. I. Stankevich, I. V. Stankevich, and N. S. Zefirov, “Topological indices in organic chemistry,” Russ. Chem. Rev., vol. 57, no. 3, p. 191, 1988. https://doi.org/10.1070/rc1988v057n03abeh003344.Suche in Google Scholar

[22] M. Randic, “Characterization of molecular branching,” J. Am. Chem. Soc., vol. 97, no. 23, pp. 6609–6615, 1975. https://doi.org/10.1021/ja00856a001.Suche in Google Scholar

[23] L. Kier, Molecular Connectivity in Chemistry and Drug Research, 1st ed. Cambridge, Academic Press, 1976.Suche in Google Scholar

[24] L. B. Kier and L. H. Hall, Molecular Connectivity in Structure-Activity Analysis, Letchworth, Hertfordshire, England and New York, Research Studies Press and Wiley, 1986.Suche in Google Scholar

[25] Z. Mihalic and N. Trinajstic, “A graph-theoretical approach to structure-property relationships,” J. Chem. Educ., vol. 69, no. 9, 1992, https://doi.org/10.1021/ed069p701.Suche in Google Scholar

[26] N. Trinajstic, Chemical Graph Theory, Florida, USA, CRC Press, 2019.10.1201/9781315139111Suche in Google Scholar

[27] E. Estrada, L. Torres, L. Rodriguez, and I. Gutman, “An atom-bond connectivity index: modelling the enthalpy of formation of alkanes,” Indian J. Chem., vol. 37A, pp. 849–855, 1998.Suche in Google Scholar

[28] A. Ali, K. C. Das, D. Dimitrov, and B. Furtula, “Atom-bond connectivity index of graphs: a review over extremal results and bounds,” Discrete Math. Lett., vol. 5, no. 1, pp. 68–93, 2021.10.47443/dml.2020.0069Suche in Google Scholar

[29] A. Ali, S. Noureen, A. Moeed, N. Iqbal, and T. S. Hassan, “Fixed-order chemical trees with given segments and their maximum multiplicative sum zagreb index,” Mathematics, vol. 12, no. 8, p. 1259, 2024. https://doi.org/10.3390/math12081259.Suche in Google Scholar

[30] R. Huang, M. F. Hanif, M. F. Hanif, M. K. Siddiqui, T. Noor, and D. Abalo, “Analyzing topological indices and heat of formation for copper (II) fluoride network via curve fitting models,” Appl. Artif. Intell., vol. 38, no. 1, p. 2327235, 2024. https://doi.org/10.1080/08839514.2024.2327235.Suche in Google Scholar

[31] R. R. Huang, S. Aftab, S. Noureen, and A. Aslam, “Analysis of porphyrin, PETIM and zinc porphyrin dendrimers by atom-bond sum-connectivity index for drug delivery,” Mol. Phys., vol. 121, no. 15, p. e2214073, 2023. https://doi.org/10.1080/00268976.2023.2214073.Suche in Google Scholar

[32] S. Noureen, A. Ali, A. A. Bhatti, A. M. Alanazi, and Y. Shang, “Predicting enthalpy of formation of benzenoid hydrocarbons and ordering molecular trees using general multiplicative Zagreb indices,” Heliyon, vol. 10, no. 10, 2024, https://doi.org/10.1016/j.heliyon.2024.e30913.Suche in Google Scholar PubMed PubMed Central

[33] S. Noureen and A. Ahmad Bhatti, “On the trees with given matching number and the modified first Zagreb connection index,” Iran. J. Math. Chem., vol. 12, no. 3, pp. 127–138, 2021.Suche in Google Scholar

[34] J. B. Liu, B. R. Liu, and C. C. Lee, “Social network analysis of regional transport carbon emissions in China: based on motif analysis and exponential random graph model,” Sci. Total Environ., 2024, https://doi.org/10.1016/j.scitotenv.2024.176183.Suche in Google Scholar PubMed

[35] B. Lucic, N. Trinajstic, and B. Zhou, “Comparison between the sum-connectivity index and product-connectivity index for benzenoid hydrocarbons,” Chem. Phys. Lett., vol. 475, nos. 1–3, pp. 146–148, 2009. https://doi.org/10.1016/j.cplett.2009.05.022.Suche in Google Scholar

[36] B. Lucic, S. Nikolic, N. Trinajstic, B. Zhou, and S. I. Turk, “Sum-connectivity index,” in Novel Molecular Structure Descriptors-Theory and Applications, vol. I, I. Gutman and B. Furtula, Ed.,Kragujevac, University of Kragujevac, 2010, pp. 101–136.Suche in Google Scholar

[37] M. Randic, “The connectivity index 25 years after,” J. Mol. Graph. Model., vol. 20, no. 1, pp. 19–35, 2001. https://doi.org/10.1016/s1093-3263(01)00098-5.Suche in Google Scholar PubMed

[38] M. Randic, “On history of the Randic index and emerging hostility toward chemical graph theory,” MATCH Commun. Math. Comput. Chem., vol. 59, no. 1, pp. 5–124, 2008.Suche in Google Scholar

[39] K. C. Das, I. Gutman, and B. Furtula, “On atom-bond connectivity index,” Chem. Phys. Lett., vol. 511, nos. 4–6, pp. 452–454, 2011. https://doi.org/10.1016/j.cplett.2011.06.049.Suche in Google Scholar

[40] A. Ali, I. Gutman, and I. Redžepovic, “Atom-bond sum-connectivity index of unicyclic graphs and some applications,” Electron. J. Math., vol. 5, pp. 1–7, 2023.10.47443/ejm.2022.039Suche in Google Scholar

[41] A. M. Albalahi, Z. Du, and A. Ali, “On the general atom-bond sum-connectivity index,” AIMS Math., vol. 8, no. 10, pp. 23771–23785, 2023. https://doi.org/10.3934/math.20231210.Suche in Google Scholar

[42] G. Yu, S. Aftab, S. Noureen, A. Aslam, and F. Tchier, “Topological characterization of PETAA and bismuth (III) iodide: flair drug carriers and therapeutic agents,” Phosphorus, Sulfur, Silicon Relat. Elem., vol. 199, no. 6, pp. 496–504, 2024. https://doi.org/10.1080/10426507.2024.2384730.Suche in Google Scholar

[43] K. C. Das, A. S. Çevik, I. N. Cangul, and Y. Shang, “On Sombor index,” Symmetry, vol. 13, no. 1, p. 140, 2021. https://doi.org/10.3390/sym13010140.Suche in Google Scholar

[44] J. Rada, J. M. Rodríguez, and J. M. Sigarreta, “General properties on Sombor indices,” Discret. Appl. Math., vol. 299, pp. 87–97, 2021, https://doi.org/10.1016/j.dam.2021.04.014.Suche in Google Scholar

[45] R. Cruz, I. Gutman, and J. Rada, “Sombor index of chemical graphs,” Appl. Math. Comput., vol. 399, p. 126018, 2021, https://doi.org/10.1016/j.amc.2021.126018.Suche in Google Scholar

[46] K. J. Gowtham and S. N. Narasimha, “On Sombor energy of graphs,” Nanosyst.: Phys. Chem. Math., vol. 12, no. 4, pp. 411–417, 2021.10.17586/2220-8054-2021-12-4-411-417Suche in Google Scholar

[47] Z. Samiei and F. Movahedi, “Investigating graph invariants for predicting properties of chemical structures of antiviral drugs,” Polycyclic Aromat. Compd., pp. 1–18, 2023, https://doi.org/10.1080/10406638.2023.2283625.Suche in Google Scholar

[48] H. Deng, Z. Tang, and R. Wu, “Molecular trees with extremal values of Sombor indices,” Int. J. Quantum Chem., vol. 121, no. 11, p. e26622, 2021. https://doi.org/10.1002/qua.26622.Suche in Google Scholar

[49] Z. Tang, Q. Li, and H. Deng, “Trees with extremal values of the Sombor index-like graph invariants,” MATCH Commun. Math. Comput. Chem., vol. 90, pp. 203–222, 2023, https://doi.org/10.46793/match.90-1.203t.Suche in Google Scholar
Received: 2024-11-22
Accepted: 2025-01-22
Published Online: 2025-02-10
Published in Print: 2025-03-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Chemical Physics
  3. Mathematical modeling for the potential energy of the aminophenol derivative azomethine molecule via Bezier surfaces and fuzzy inference system
  4. Topological descriptors and connectivity analysis of coronene fractal structures: insights from atom-bond sum-connectivity and Sombor indices
  5. Fundamental Concepts of Physical Science
  6. Stability analysis of semi-analytical technique for time-fractional Cauchy reaction-diffusion equations
  7. Dynamics of closed-form invariant solutions and formal Lagrangian approach to a nonlinear model generated by the Jaulent–Miodek hierarchy
  8. Solid State Physics & Materials Science
  9. Temperature-dependent elastic, mechanical, thermal, and acoustic behavior in alkaline earth semiconductors
  10. Investigation of the effect of Si content on the structural, mechanical, and tribological properties of TiAlN/AlSi protective multilayers
  11. Thermodynamics & Statistical Physics
  12. Higher-order corrections on the denaturation of homogeneous DNA thermodynamics
https://doi.org/10.1515/zna-2024-0286
Schlagwörter für diesen Artikel
topological index; chemical graph theory; ABS-index and invariants of Sombor index; coronene fractals

Artikel in diesem Heft

  1. Frontmatter
  2. Chemical Physics
  3. Mathematical modeling for the potential energy of the aminophenol derivative azomethine molecule via Bezier surfaces and fuzzy inference system
  4. Topological descriptors and connectivity analysis of coronene fractal structures: insights from atom-bond sum-connectivity and Sombor indices
  5. Fundamental Concepts of Physical Science
  6. Stability analysis of semi-analytical technique for time-fractional Cauchy reaction-diffusion equations
  7. Dynamics of closed-form invariant solutions and formal Lagrangian approach to a nonlinear model generated by the Jaulent–Miodek hierarchy
  8. Solid State Physics & Materials Science
  9. Temperature-dependent elastic, mechanical, thermal, and acoustic behavior in alkaline earth semiconductors
  10. Investigation of the effect of Si content on the structural, mechanical, and tribological properties of TiAlN/AlSi protective multilayers
  11. Thermodynamics & Statistical Physics
  12. Higher-order corrections on the denaturation of homogeneous DNA thermodynamics
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