Novel Fuzzy Topological Descriptors for Characterizing Aromatic Hydrocarbons

Ghods, Masoud; Hasani, Mehri

doi:10.22075/ijnaa.2026.37395.5442

Novel Fuzzy Topological Descriptors for Characterizing Aromatic Hydrocarbons

Document Type : Research Paper

Authors

masoud ghods ¹

Mehri Hasani ²

¹ Faculty of Mathematics, Statistics and Computer Science, Semnan University, Semnan, Iran

² Department of Mathematics, Statistics, and Computer Science, Semnan University, 35131-19111, Iran

10.22075/ijnaa.2026.37395.5442

Abstract

Fuzzy graphs have gained significant attention in diverse scientific fields, including mathematics and chemistry, owing to their superior accuracy and adaptability compared to conventional models. This study delves into a theoretical exploration of the fuzzy graph representation of aromatic hydrocarbons, focusing on the computation of several fuzzy-based degree topological indices. Novel definitions are introduced for the first Zagreb fuzzy index, Forgotten index, and Y-index, alongside a generalized formula for fuzzy topological indices of linear and cyclic aromatic hydrocarbons, incorporating edge degrees. Moreover, a comprehensive formula is derived to calculate specific topological indices of hydrocarbons based on the number of benzene rings. This methodology empowers researchers to predict and estimate compounds' physical and chemical properties by leveraging topological indices and precise calculations of bond lengths and atomic masses facilitated by computational software.

Keywords

Fuzzy graph

Topological indices

Zagreb index

Randic index

Aromatic hydrocarbons

[1] A. Alameri, N. Al-Naggar, M. Al-Rumaima, and M. Alsharafi, Y-index of some graph operations, International Journal of Applied Engineering Research (IJAER) 15 (2020), no. 2, 173–179.

[2] M. Binu, S. Mathew, and J. N. Mordeson, Connectivity index of a fuzzy graph and its application to human trafficking, Fuzzy Sets and Systems 360 (2019), 117–136.

[3] J. A. Bondy, U. S. R. Murty, et al. , Graph theory with applications, vol. 290, Macmillan London, 1976.

[4] H. M. Fraz, K. Ali, and M. F. Nadeem, Entropy measures of silicon nanotubes using degree based topological indices, Physica Scripta 100 (2025), no. 1, 015202.

[5] B. Furtula and I. Gutman, A forgotten topological index, Journal of mathematical chemistry 53 (2015), no. 4, 1184–1190.

[6] D. Gómez González, F. J. Montero De Juan, and F. J. Yáñez Gestoso, A coloring fuzzy graph approach for image classification, (2006).

[7] J. L. Gross and J. Yellen, Handbook of graph theory, CRC press, 2003.

[8] I. Gutman, J. Kennedy, and L. Quintas, Perfect matchings in random hexagonal chain graphs, Journal of mathematical chemistry 6 (1991), no. 1, 377–383.

[9] M. Hasani and M. Ghods, Calculation of topological indices along with matlab coding in qspr analysis of calcium channel-blocking cardiac drugs, Journal of Mathematical Chemistry 62 (2024), no. 10, 2456–2477.

[10] , Investigating fuzzy topological indices of linear and cyclic anthracene hydrocarbon, Fuzzy Optimization and Modeling Journal (FOMJ) 5 (2024), no. 4, 1–19.

[11] , Predicting the physicochemical properties of drugs for the treatment of parkinson's disease using topological indices and matlab programming, Molecular Physics 122 (2024), no. 9, e2270082.

[12] , Topological indices and qspr analysis of some chemical structures applied for the treatment of heart patients, International Journal of Quantum Chemistry 124 (2024), no. 1, e27234.

[13] , Computing some fuzzy topological indices of linear and multi-cyclic tetracene hydrocarbon, Journal of Discrete Mathematical Sciences & Cryptography (2025), 1–18.

[14] , Investigating fuzzy topological indices of linear and multi-cyclic naphtalene, Journal of Interdisciplinary Mathematics 28 (2025), no. 5, 1779–1793.

[15] , Qspr analysis of kidney infection (pyelonephritis) drugs by entropy graphs weighted with topological indices, and matlab programming, Polycyclic Aromatic Compounds 45 (2025), no. 6, 1011–1035.

[16] , A multi–criteria decision–making approach for ranking antiepileptic drugs using topological indices, International Journal of Information Technology & Decision Making 25 (2026), no. 07, 2399–2424.

[17] S. Hayat and M. Imran, On degree based topological indices of certain nanotubes, Journal of Computational and Theoretical Nanoscience 12 (2015), no. 8, 1599–1605.

[18] S. Iijima, Helical microtubules of graphite carbon, Nature 56 (1999), 354.

[19] S. R. Islam and M. Pal, First zagreb index on a fuzzy graph and its application, Journal of Intelligent & Fuzzy Systems 40 (2021), no. 6, 10575–10587.

[20] , Hyper-wiener index for fuzzy graph and its application in share market, Journal of Intelligent & Fuzzy Systems 41 (2021), no. 1, 2073–2083.

[21] , F-index for fuzzy graph with application, TWMS Journal of Applied and Engineering Mathematics (2023).

[22] , Hyper-connectivity index for fuzzy graph with application. , TWMS Journal of Applied & Engineering Mathematics 13 (2023), no. 3, 920.

[23] S. T. Jalali and M. Ghods, Computing y-index for some special graph, J. Disc. Math. Sci. Cryto 26 (2022), no. 4, 967–976.

[24] S. Kalathian, S. Ramalingam, S. Raman, and N. Srinivasan, Some topological indices in fuzzy graphs, Journal of Intelligent & Fuzzy Systems 39 (2020), no. 5, 6033–6046.

[25] J. N. Mordeson and S. Mathew, Advanced topics in fuzzy graph theory, vol. 375, Springer, 2019.

[26] M. Pal, S. Samanta, and G. Ghorai, Modern trends in fuzzy graph theory, Springer, 2020.

[27] V. N. Popov, Carbon nanotubes: properties and application, Materials Science and Engineering: R: Reports 43 (2004), no. 3, 61–102.

[28] S. Poulik, S. Das, and G. Ghorai, Randic index of bipolar fuzzy graphs and its application in network systems, Journal of Applied Mathematics and Computing 68 (2022), no. 4, 2317–2341.

[29] S. Poulik and G. Ghorai, Certain indices of graphs under bipolar fuzzy environment with applications, Soft Computing 24 (2020), no. 7, 5119–5131.

[30] J. Rada, O. Araujo, and I. Gutman, Randic index of benzenoid systems and phenylenes, Croatica Chemica Acta 74 (2001), no. 2, 225–235.

[31] A. Rosenfeld, Fuzzy graphs, Fuzzy sets and their applications to cognitive and decision processes, Elsevier, 1975, pp. 77–95.

[32] X. Shi, S. Kosari, A. A. Talebi, S. H. Sadati, and H. Rashmanlou, Investigation of the main energies of picture fuzzy graph and its applications, International Journal of Computational Intelligence Systems 15 (2022), no. 1, 31.