The M-Polynomial and Nirmala index of Certain Composite Graphs

Main Article Content

Akar H. Karim
Nabeel E. Arif
Ayad M. Ramadan

Abstract

The M-Polynomial and Nirmala index are considered as two of the most recent found and important subjects in chemical graph theory. In this paper we drive and prove the computing formula of Nirmala index from the M-Polynomial, then compute the M-Polynomial for some certain composite graphs, and the Nirmala index via the computed M-Polynomial. The composite graphs are new defined graphs Kn(Pt)Km , Cn(e)Kn , and others obtained from simple graphs by certain graph operations such as join, corona, and cluster of any graph with some special graphs such as complete, path, …etc

Article Details

How to Cite
Akar H. Karim, Nabeel E. Arif, & Ayad M. Ramadan. (2022). The M-Polynomial and Nirmala index of Certain Composite Graphs. Tikrit Journal of Pure Science, 27(3), 92–101. https://doi.org/10.25130/tjps.v27i3.45
Section
Articles

References

[1] Chartrand, G. and Zhang, P. (2008). Chromatic graph theory. Chapman and Hall/CRC: 483 pp.

[2] Alikhani, S.; Hasni, R. and Arif, N.E. (2014). On the atom-bond connectivity index of some families of dendrimers. Journal of Computational and Theoretical Nanoscience, 11(8):1802-1805.

[3] Dong, F.M.; Koah, K.M. and Teo, K.L. (2005). Chromatic polynomials and chromaticity of graphs. World Scientific: 356 pp.

[4] Vasudev, C. (2006). Graph theory with applications. New Age International: 466 pp. [5] Zwillinger, D. (2018). CRC standard mathematical tables and formulas. chapman and hall/CRC: 858 pp.

[6] Stevanovic, D. (2001). Hosoya polynomial of composite graphs. Discrete mathematics, 235(1-3):237-244.

[7] Arif, N.E.; Karim, A.H. and Hasni, R. (2022). Sombor index of some graph operations. International Journal of Nonlinear Analysis and Applications, 13(1):2561-2571.

[8] Deutsch, E. and Klavžar, S. (2014).M-polynomial and degree-based topological indices. arXiv preprint arXiv:1407.1592.

[9] Khalaf, A.J.M. et al. (2020). M-Polynomial and topological indices of book graph. Journal of Discrete Mathematical Sciences and Cryptography, 23(6):1217-1237.

[10] Chaudhry, F. et al. (2021). On computation of M-Polynomial and topological indices of starphene graph. Journal of Discrete Mathematical Sciences and Cryptography, 24(2):401-414.

[11] Basavanagoud, B.; Barangi, A.P. and Jakkannavar, P. (2019). M-polynomial of some graph

operations and cycle related graphs. Iranian Journal of Mathematical Chemistry, 10(2):127-150.

[12] Raza, Z. et al. (2020). M-polynomial and degree based topological indices of some nanostructures. Symmetry, 12(5):831.

[13] Afzal, F. et al. (2020). Some new degree based topological indices via m-polynomial. Journal of Information and Optimization Sciences, 41(4):1061-1076.

[14] Cancan, M, et al. (2020). Some new topological indices of silicate network via m-polynomial. Journal of Discrete Mathematical Sciences and Cryptography, 23(6):1157-1171.

[15] Kulli. V.R. (2021). Nirmala index. International Journal of Mathematics Trends and Technology, 67(3):8-12.

[16] Kulli. V.R. and Gutman, I. (2021). On some mathematical properties of nirmala index. Annals of pure and Applied Mathematics, 23(2):93-99.

[17] Gutman, I.; Kulli. V.R. and Redzepovic, I. (2021). Nirmala index of kragujevac trees. International Journal of Mathematics Trends and Technology, 67(6):44–49.

[18] Kulli. V.R. (2021). Different versions of nirmala index of certain chemical structures. International Journal of Mathematics Trends and Technology, 67(7):56–63.

[19] Kulli. V.R. (2021). On multiplicative inverse nirmala indices. Annals of Pure and Applied Mathematics, 23(2):57–61.

[20] Gutman, I. and Kulli, V.R. (2021). Nirmala energy. Open Journal of Discrete Applied Mathematics, 4(2):11–16.