Topological Properties of Bismuth tri-iodide Using Neighborhood M-Polynomial

	International Journal of Mathematics Trends and Technology (IJMTT)
	© 2019 by IJMTT Journal
	Volume-65 Issue-10
	Year of Publication : 2019
	Authors : A.Verma, S.Mondal, N.De, A.Pal
	10.14445/22315373/IJMTT-V65I10P512

MLA Style:A.Verma, S.Mondal, N.De, A.Pal  Topological Properties of Bismuth tri-iodide Using Neighborhood M-Polynomial" International Journal of Mathematics Trends and Technology 65.10 (2019):83-90 .

APA Style: A.Verma, S.Mondal, N.De, A.Pal (2019). Topological Properties of Bismuth tri-iodide Using Neighborhood M-Polynomial International Journal of Mathematics Trends and Technology,83-90

Abstract
Anoutstanding way of findingneighborhood degree sum based topological indices is neighborhood M-polynomial. The bismuth tri-iodide BiI3 is a wide band gap layered semiconductor with several optical properties.In this paper, the neighborhood M-polynomial of bismuth tri-iodide chain and sheet are obtained. Some topological indices based on neighbourhood degree sum are recovered from the neighbourhood M-polynomial. Also, the findings are interpreted graphically.

Reference

[1] H. Wiener, ―Structural determination of the paraffin boiling points‖,J. Am. Chem. Soc., vol. 69, no. 1, pp. 17-20, 1947.
[2] S. M. Hosamani, ―Computing Sanskruti index of certain nanostructures‖, J. Appl. Math. Comput., vol. 54, pp. 425-433, 2017.
[3] M. Ghorbani and M. A. Hosseinzadeh, ―The third version of Zagreb index‖, Discrete Math. Algorithms Appl., vol. 5, 2013, doi: 10.1142/S1793830913500390.
[4] V. R. Kulli,‖ Neighborhood Indices of Nanostructures‖, International Journal of Current Research in Science and Technology, vol. 5, no. 3, pp. 1-14, 2019.
[5] V. R. Kulli, ―Multiplicative Neighborhood Indices‖, Annuls of Pure and Applied Mathematics, vol. 1x, 2019, doi: 10.22457/apam.614v19n2a6.
[6] S. Mondal, N. De and A. Pal, ―On Neighbourhood Zagreb index of product graphs‖, Preprint, arXiv:1805.05273, 2018.
[7] S. Mondal, N. De and A. Pal, ―On some new neighbourhood degree based indices‖, ActaChemica Iasi, vol. 27, no. 1, pp. 31-46, 2019.
[8] S. Mondal, N. De and A. Pal, ―QSPR analysis of some novel neighborhood degree based topological descriptors‖, Preprint,arXiv: 1906.06660.
[9] I. Gutman, ―Some properties of the Wiener polynomials‖, Graph Theory Notes N.Y., vol. 125, pp. 13-18, 1993.
[10] V. Alamian, A. Bahrami and B. Edalatzadeh, ―PI Polynomial of V-Phenylenic nanotubes and nanotori‖, Int. J. Mole. Sci., vol. 9, no. 3, pp. 229-234, 2008, doi: 10.3390/ijms9030229.
[11] M. R. Farahani, ―Computing theta polynomial, and theta index of V-phenylenic planar, nanotubes and nanotoris‖, Int. J. Theoretical Chem., vol. 1, no. 1, pp. 1-9, 2013.
[12] E. Deutsch and S. Klavzar, ―M-Polynomial, and degree-based topological indices‖, Iran. J. Math. Chem., vol. 6, pp. 93-102, 2015.
[13] Y. C. Kwun, M. Munir, W. Nazeer, S. Rafque and S. M. Kang, ―M Polynomials and topological indices of V-Phenylenic Nanotubes and Nanotori‖, Scientific Reports, vol. 7, 2017, doi:10.1038/s41598-017-08309-y.
[14] S. Mondal, N. De, and A. Pal, ―The M-Polynomial of Line graph of Subdivision graphs‖, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat, vol. 68, no. 2, pp. 2104-2116, 2019.
[15] S. Mondal, N. De and A. Pal, ―Neighborhood M-polynomial of crystallographic structures‖, Preprint.
[16] A. Cuna, I. Aguiar, A. Gancharov, M.E.P. Barthaburu, and L. Fornaro, ―Correlation between growth orientation and growth temperature for bismuth tri‐iodide films‖, Cryst. Res. Technol., vol. 39, no. 10, pp. 899-905, 2004.
[17] A. Cuna, A. Noguera, E. Saucedo, and L. Fornaro, ―Growth of bismuth tri‐iodide platelets by the physical vapor deposition method‖, Cryst. Res. Technol., vol. 39, no. 10, pp. 912-919, 2004.
[18] K. Watanabe, T. Karasawa, T. Komatsu, and Y. Kaifu, ―Optical properties of extrinsic two-dimensional excitons in BiI₃ single crystals‖, J. Phys. Soc. Jpn., vol. 55, pp. 897-907, 1986.
[19] R.W.G. Wyckoff, Crystal Structures, 2nd ed.; John Wiley & Sons, Inc.: New York, NY, USA; London, UK; Sydney, Australia, 1964.
[20] H. Yorikawa and S. Muramatsu, ―Theoretical Study of Crystal and Electronic Structures of BiI₃", J. Phys. Condens. Matter, vol. 20, pp. 325–335, 2008.

Keywords
Graph,Bismuth tri-iodide,Neighborhood M-polynomial, Topological index.