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Discontinuity, Nonlinearity, and Complexity 13(2) (2024) 361--371 | DOI:10.5890/DNC.2024.06.013

Jaber Ramezani Tousi, Masoud Ghods

Department of applied mathematics, Semnan University, 35131-19111, Iran

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Abstract

Glass is an amorphous non-crystalline solid and often transparent that has wide applications in architecture, tableware, optics, and optoelectronics. \newline In this article, first, the mathematical relationship between M-polynomial and topological indices such as Revan indices, Gourava indices, and Y-index are obtained. Then M-polynomial is computed for the molecular graph and the line graph of Glass. Finally, using M-polynomial, Revan indices, Gourava indices, and Y-index are calculated.

References

1. [1]	Elkadi, H. (2006), Cultures of Glass Architecture, Routledge.

2. [2]	Varshneya, A.K. (2006), Fundamentals of Inorganic Glasses, Society of Glass Technology, Elsevier.

3. [3]	Chrisey, D.B. and Hubler, G.K. (1994), Pulsed Laser Deposition of Thin Films, Ed., John Wiley \& Sons: New York.

4. [4]	Richert, R. (2002), Heterogeneous dynamics in liquids: fluctuations in space and time, Journal of Physics: Condensed Matter, 14(23), R703-R738.

5. [5]	Koch, C.C. (1996), Amorphization of single composition powders by mechanical milling, Scripta materialia, 34(1), 21-27.

6. [6]	Andrianov, N.T. (2003), Sol-gel method in material technology, Glass Ceramics, 60, 9-10, 320-325.

7. [7]	Jones, R.W. (1989), Fundamental Principles of Sol-Gel Technology, The Institute of Metals: London.

8. [8]	Trachenko, K. (2004), Understanding resistance to amorphization by radiation damage, Journal of Physics: Condensed Matter, 16(9), R1491-R1515.

9. [9]	Weber, W.J. (2000), Models and mechanisms of irradiation-induced amorphization in ceramics, Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, 166(2000), 98-106.

10. [10]	Greaves, G.N., Meneau, F., Sapelkin, A., Colyer, L.M., Ap Gwynn, I., Wade, S., and Sankar, G. (2003), The rheology of collapsing zeolites amorphized by temperature and pressure, Nature Materials, 2(9), 622-629.

11. [11]	Mishima, O., Calvert, L.D., and Whalley, E.M. (1984), A new method of making amorphous solids, Nature, 310(5076), 393-395.

12. [12]	Deutsch, E. and Klavzar, S. (2015), M-polynomial and degree-based topological indice, Iranian Journal of Mathematical Chemistry, 6(2), 93-102.

13. [13]	Hussain, S., Afzal, F., Afzal, D., Cancan, M., Ediz, S., and Farahani, M.R. (2021), Analyzing the boron triangular nanotube through topological indices via M --polynomial, Journal of Discrete Mathematical Sciences and Cryptography, 24(2), 415-426.

14. [14]	Raheem, A., Javaid, M., The, W.C., Wang, S., and Liu, J.B. (2020), M-polynomial method for topological indices of 2D-lattice of three-layered single-walled titania nanotubes, Journal of Information and Optimization Sciences, 41(3), 743-753.

15. [15]	Kulli, V.R. (2017), The Gourava indices and coindices of graphs, Annals of Pure and Applied Mathematics, 14(1), 33-38.

16. [16]	Kulli, V.R. (2017), Revan indices of oxide and honeycomb networks, International Journal of Mathematics And its Applications, 5(4), 663- 667.

17. [17]	Alameri, A., Al Naggar, N., Al-Rumaima, M., and Alsharafi, M. (2020), Y-index of some graph operations, International Journal of Applied Engineering Research, 7(2), 173-179.

18. [18]	Kulli, V.R., Pal, M., Samanta, S., and Pal A. (2020), Handbook of Research of Advanced Applications of Graph Theory in Modern Society, Global, Hershey.