Investigating Fuzzy Topological indices of Linear and Cyclic Anthracene Hydrocarbon
الموضوعات : Fuzzy Optimization and Modeling Journal
Mehri Hasani
1
,
Masoud Ghods
2
1 - Department of Mathematics, Statistics, and Computer Science, Semnan University
2 - Department of Mathematics, Statistics, and Computer Science, Semnan University
الکلمات المفتاحية: Fuzzy graph, Topological indices, Zagreb index, Randic index, Molecular structure, Vertex degree,
ملخص المقالة :
This research focuses on the theoretical examination of the fuzzy graph of aromatic hydrocarbon of Anthracene and computes several fuzzy-based degree topological indices. The research introduces new definitions for the first Zagreb fuzzy index, forgotten index, and Y−index, and provides a general formula for fuzzy topology indices of Anthracene hydrocarbon by considering the degree of each edge. Moreover, a general formula is presented to determine the specific topology index of a hydrocarbon-based on the number of rows and columns. We compared the topological indices of linear Anthracene and found that the Randic and harmonic indices had the highest values. Continuing with the drawing of the Randic index surface, we concluded that when the number of parameters in the rows and columns of the Anthracene hydrocarbon is equal, the Randic index has the highest value. This approach can help researchers predict and estimate compounds' physical and chemical properties using topology indices and precise bond lengths and atomic mass calculations through software.
1. Abdo, H., Dimitrov, D., Gutman, I. (2017). On extremal trees with respect to the F-index. Kuwait Journal of Science.
2. Akhtar, S., Imran, M., Farahani, M. R. (2011). Extremal unicyclic and bicyclic graphs with respect to the F-index. 80-91.
3. Alameri, A., Al-Naggar, N., Al-Rumaima, M., & Alsharafi, M. (2020). Y-index of some graph operations. International Journal of Applied Engineering Research (IJAER), 15(2), 173-179.
4. Amin, R., Nayeem, S. M. A. (2018). On the F-index and F-coindex of the line graphs of the subdivision graphs. Malaya J. Matematic, 362-368.
5. Azeem M, Anwar S, Jamil MK, Saeed M, D. M. (2024). Topological numbers of fuzzy soft graphs and their application. Information Sciences, 667, 120468.
6. Bhattacharya, P. (1987). Some remarks on fuzzy graphs. Pattern Recognition Letters, 6(5), 297–302.
7. Bhutani, K. R. (1989). On automorphisms of fuzzy graphs. Pattern Recognition Letters, 9(3), 159–162.
8. Binu, M., Mathew, S., Mordeson, J. N. (2019). Connectivity index of a fuzzy graph and its application to human trafficking. Fuzzy Sets and Systems, 117-136.
9. Furtula, B., Graovac, A., & Vukičević, D. (2010). Augmented Zagreb index. Journal of Mathematical Chemistry, 48(2), 370-380.
10. Furtula, B., & Gutman, I. (2015). A forgotten topological index. Journal of Mathematical Chemistry, 53(4), 1184-1190.
11. Gani, A. N., & Ahamed, M. B. (2003). Order and size in fuzzy graphs. Bulletin of Pure and Applied Sciences, 22(1), 145–148.
12. Gómez, D., Montero, J., & Yáñez, J. (2006). A coloring fuzzy graph approach for image classification. Information Sciences, 176(24), 3645-3657.
13. Gross, J. L., Yellen, J. (2005). Handbook of graph theory. In Choice Reviews Online (Vol. 42, Issue 05).
14. Gupta, C.K., Lokesha, V., Shwetha, S.B. and Ranjini, P. S. (2016). On the Symmetric Division deg Index of Graph. Southeast Asian Bulletin of Mathematics, 40.
15. Gutman, I., & Trinajstić, N. (1972). Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons. Chemical Physics Letters, 17(4), 535–538.
16. Hasani, M., & Ghods, M. (2024). QSPR Analysis of Kidney Infection (Pyelonephritis) Drugs by Entropy Graphs Weighted with Topological Indices, and MATLAB Programming. Polycyclic Aromatic Compounds, 1-25.
17. Hasani, M., & Ghods, M. (2024). Predicting the physicochemical properties of drugs for the treatment of Parkinson’s disease using topological indices and MATLAB programming. Molecular Physics, 122(9).
18. Hasani, M., & Ghods, M. (2024). Topological indices and QSPR analysis of some chemical structures applied for the treatment of heart patients. International Journal of Quantum Chemistry, 124(1), e27234.
19. Hasani, M., & Ghods, M. (2024). Calculation of topological indices along with MATLAB coding in QSPR analysis of calcium channel-blocking cardiac drugs. Journal of Mathematical Chemistry, 1-22.
20. Hasani, M., & Ghods, M. (2023). M-polynomials and topological indices of porphyrin-cored dendrimers. Chem. Methodol, 7, 288-306.
21. Hayat, S., Imran, M. (2015). On degree based topological indices of certain nanotubes. Journal of Computational and Theoretical Nanoscience, 1599-1605.
22. Hosamani, S. M. (2017). Deepa perigidad, shruti jamagoud yallavva maled and sharada gavade, QSPR anlysis of certain degree based topological indices. Journal of Applied Probability and Statistics, 361-371.
23. Iijima, S. (1991). Helical microtubules of graphitic carbon. Nature, 354(6348), 56-58.
24. Islam, S. K. R., & Pal, M. (2023). F-Index for Fuzzy Graph With Application. Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, 13(2), 517–530.
25. Islam, S. R., & Pal, M. (2021). First Zagreb index on a fuzzy graph and its application. Journal of Intelligent and Fuzzy Systems, 40(6), 10575–10587.
26. Islam, S. R., & Pal, M. (2021). Hyper-Wiener index for fuzzy graph and its application in share market. Journal of Intelligent and Fuzzy Systems, 41(1), 2073–2083.
27. Islam, S. R., & Pal, M. (2023). Hyper-Connectivity Index for Fuzzy Graph With Application. Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, 13(3), 920–936.
28. Jalali, S. T., & Ghods, M. (2023). Computing Y-index for some special graph. Journal of Discrete Mathematical Sciences and Cryptography, 26(4), 967–976.
29. Kalathian, S., Ramalingam, S., Raman, S., & Srinivasan, N. (2020). Some topological indices in fuzzy graphs. Journal of Intelligent and Fuzzy Systems, 39(5), 6033–6046.
30. Kosari, S., Qiang, X., Kacprzyk, J., Ain, Q. T., & Rashmanlou, H. (2024). A Study on Topological Indices in Fuzzy Graphs with Application in Decision Making Problems. Journal of Multiple-Valued Logic and Soft Computing, 42(5–6), 567–589.
31. Li, X., & Gutman, I. (2024). Mathematical Aspects of Randic-Type Molecular Structure Descriptors, Mathematical Chemistry Monographs No. 1, Kragujevac, 2006, pp. Scientific Reports, 14, 10933.
32. Maji, D., & Ghorai, G. (2020). Computing F-index, coindex and Zagreb polynomials of the kth generalized transformation graphs. Heliyon, 6(12).
33. Mondal, S., De, N., Pal, A. (2019a). On some new neighbourhood degree based indices. Acta Chem. Iasi., 31–46.
34. Mondal, S., De, N., Pal, A. (2019b). Topological properties of Graphene using some novel neighborhood degree-based topological indices. International Journal of Mathematics for Industry, 1950006.
35. Mondal, S., De, N., & Pal, A. (2021). On neighborhood Zagreb index of product graphs. Journal of Molecular Structure, 12-23.
36. Mufti, Z. S., Anjum, R., Tawfiq, F. M. O., Tabraiz, A., Xin, Q., & Akter, D. (2023). Fuzzy Topological Characterization of qCn Graph via Fuzzy Topological Indices. Journal of Mathematics, 2023, 5141179.
37. Mufti, Z. S., Fatima, E., Anjum, R., Tchier, F., Xin, Q., & Hossain, M. M. (2022). Computing First and Second Fuzzy Zagreb Indices of Linear and Multiacyclic Hydrocarbons. Journal of Function Spaces, 2022.
38. Nagoor Gani, A., & Latha, S. R. (2012). On irregular fuzzy graphs. Applied Mathematical Sciences, 6(9-12), 517-523.
39. Pal, M., Samanta, S., & Ghorai, G. (2020). Modern Trends in Fuzzy Graph Theory. In Modern Trends in Fuzzy Graph Theory, 7-93.
40. Parveen, S., Hassan Awan, N. U., Mohammed, M., Farooq, F. B., & Iqbal, N. (2022). Topological Indices of Novel Drugs Used in Diabetes Treatment and Their QSPR Modeling. Journal of Mathematics, 2022.
41. Popov, V. N. (2004). properties and application. Materials Science and Engineering. Carbon Nanotubes, 43.
42. Poulik, S., Das, S., & Ghorai, G. (2022). Randic index of bipolar fuzzy graphs and its application in network systems. Journal of Applied Mathematics and Computing, 68(4), 2317–2341.
43. Poulik, S., & Ghorai, G. (2021). Determination of journeys order based on graph’s Wiener absolute index with bipolar fuzzy information. Information Sciences, 545, 608–619.
44. Rada, J., Araujo, O., & Gutman, I. (2001). Randić index of benzenoid systems and phenylenes. Croatica Chemica Acta, 74(2), 225–235.
45. Rashmanlou, H., Samanta, S., Pal, M., & Borzooei, R. A. (2016). A study on vague graphs. SpringerPlus, 5(1).
46. Rosenfeld, A. (1975). Fuzzy graphs, Fuzzy sets and their applications to cognitive and decision processes. 77–95.
47. Shailaja, K., Sameena, T., Sethy, S. P., Patil, P., & Ashraf, M. O. (2013). Carbon Nano Tube: a Review. Indian J Res Pharm Biotechnol, 5674(October), 2320–2322.
48. Shao, Z., Kosari, S., Shoaib, M., & Rashmanlou, H. (2020). Certain Concepts of Vague Graphs With Applications to Medical Diagnosis. Frontiers in Physics, 8, 357.
49. Shi, X., Kosari, S., Talebi, A. A., Sadati, S. H., & Rashmanlou, H. (2022). Investigation of the Main Energies of Picture Fuzzy Graph and its Applications. International Journal of Computational Intelligence Systems, 15(1).
50. Trinajstic, N. (2018). Chemical graph theory. CRC press.
51. Ullah, A., Bano, Z., & Zaman, S. (2024). Computational aspects of two important biochemical networks with respect to some novel molecular descriptors. Journal of Biomolecular Structure and Dynamics, 42(2), 791-805.
52. Wiener, H. (1947). Structural determination of paraffin boiling points. Journal of the American Chemical Society, 17–20.
53. Xavier, A., Theresal, S., & Raja, S. M. J. (2020). Induced H-packing k-partition number for certain nanotubes and chemical graphs. Journal of Mathematical Chemistry, 58(6), 1177-1196.
54. XU, J. (1997). The Use of Fuzzy Graphs in Chemical Structure Research. Fuzzy Logic in Chemistry, 249-282.
55. Zadeh, L. (1965). Fuzzy sets, information and control. 338–353.
