Discontinuity, Nonlinearity, and Complexity 14(1) (2025) 63--74 | DOI:10.5890/DNC.2025.03.005

Azizollah Babaei$^{1}$, AllahBakhsh Yazdani Cherati$^1$, Rohollah Yousefpour$^2$

$^{1}$ Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

$^{2}$ Department of Computer Sciences, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

Abstract

Mathematics has many applications in other sciences, especially in chemistry, where the theory of chemical graphs is one of the most important uses. Analyzing the properties dependent on the structure of different molecules is of significant importance. One of these molecules, whose structure is investigated in this article, is Bismuth tri-iodide [m, n]. In this article, we investigate the relations between the first $\delta$- Gourava index, second $\delta$- Gourava index, SK Revan index, SK1 Revan index, and SK2 Revan index via M-polynomials. These indices are then calculated for the molecular graph and the line graph of Bismuth tri-iodide [m, n], and the results are presented.

References

1. [1]	Alsulami, S., Hussain Butt, S., Afzal, F., Farahani, M., and Afzal, D. (2022), Topological Properties of Degree-Based Invariants via M-Polynomial Approach, Journal of Mathematics, 2022(4), 1-8.

2. [2]	Tousi, J.R. and Ghods, M. (2023), Computing K Banhatti and K Hyper Banhatti indices of Titania nanotubes TiO2 [m, n], Journal of Information and Optimization Sciences, 44(2), 207-216.

3. [3]	Watanabe, K., Karasawa, T., Komatsu, T., and Kaifu, Y. (1986), Optical properties of extrinsic two-dimensional excitons in BiI3 single crystals, Journal of the Physical Society of Japan, 55(3), 897-907.

4. [4]	Gutman, I., Trinajstic, N., and Wilcox, F. (1975), Graph theory and molecular orbitals. XII. Acyclic polyenes, Journal of Chemical Physics, 62(9), 3399-3405.

5. [5]	Kaladevi, V., Murugesan, R., and Pattabiraman, K. (2017), First reformulated Zagreb indices of some classes of graphs, Carpathian Mathematical Publications, 9(2), 134-144.

6. [6]	Gutman, I. and Trinajstic, N. (1972), Graph theory and molecular orbitals. Total $\pi$-electron energy of alternant hydrocarbons, Chemical Physics Letters, 17(4), 535-538.

7. [7]	Kulli, V.R. (2017), The Gourava indices and coindices of graphs, Annals of Pure and Applied Mathematics, 14(1), 33-38.

8. [8]	Kulli, V.R. (2017), On hyper Gourava indices and coindices, International Journal of Mathematical Archive, 8(12), 116-120.

9. [9]	Shigehalli, V. and Kanabur, R. (2016), Computing degree-based topological indices of polyhex nanotubes, Journal of Discrete Mathematics and its Applications, 6(1), 47-55.

10. [10]	Smart, L. and Elaine, A.M. (2005), Solid State Chemistry: An Introduction, CRC Press: Boca Raton, FL, USA.

11. [11]	Wyckoff, R.W.G. (1964), Crystal Structures, 2nd ed.; John Wiley \& Sons, Inc.: New York, NY, USA; London, UK; Sydney, Australia.

12. [12]	Nason, D. and Keller, L. (1995), The growth and crystallography of bismuth tri-iodide crystals grown by vapor transport, Journal of Crystal Growth, 156(3), 221-226.

13. [13]	Kulli, V.R. (2021), $\delta$-Banhatti, hyper $\delta$-Banhatti indices and their polynomials of certain networks, International Journal of Engineering Sciences $\&$ Research Technology, 10, 1-8.

14. [14]	Basavanagoud, B. and Policepatil, S. (2021), Chemical applicability of Gourava and hyper-Gourava indices, Nanosystems: Physics, Chemistry, Mathematics, 12, 142-150.

15. [15]	Kulli, V.R. (2017), Revan indices of oxide and honeycomb networks, International Journal of Mathematics and its Applications, 5, 663-667.

16. [16]	Mahboob, A., Muhiuddin, G., Siddique, I., and Alam, S.M. (2022), A view of Banhatti and Revan indices in chemical graphs, Journal of Mathematics, 2022(1), 1-8.

17. [17]	Ashraf, R. and Akhter, S. (2004), Revan indices and revan polynomials of silicon carbide graphs, International Journal of Engineering Research and Technology, 8(9), 353-361.

18. [18]	Deutsch, E. and Klavzar, S. (2015), M-polynomial and degree-based topological indices, Iranian Journal of Mathematical Chemistry, 6, 93-102.

19. [19]	Irfan, M., Rehman, H.U., Almusawa, H., Rasheed, S., and Baloch, I.A. (2021), M-polynomials and topological indices for line graphs of chain silicate network and h-naphtalenic nanotubes, Journal of Mathematics, 2021, 1-11.

20. [20]	Bagga, J. (2004), Old and new generalizations of line graphs, International Journal of Mathematics and Mathematical Sciences, 29(1), 1509-1521.