Volume 67 | Issue 8 | Year 2021 | Article Id. IJMTT-V67I8P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V67I8P503
Let G = (V, E) be a molecular graph with vertex set V and edge set E. The topological indices of molecular graphs are widely used for establishing relation between the structure of a molecular compound and its physicochemical properties or biological properties. The degree-based topological indices of wheel graph (W4,m), antiwheel graph(AWW5,m), gear graph (J8,m),and antiweb gear graph (AWJ8,m), are studied from M-polynomials.
[1] W.Gao, W.Wang, and M.R.Farahani, Topological indices in the study of molecular structure in anticancer drugs, Hindawi, Journal of Chemistry, (2016)Article ID 32163227.
[2] B.Basvanagoud and P.Jakkanavar, Electronic Journal of Mathematical Analysis and Applications, 8(1) (2020) 75-99.
[3] M.R.R.Kanna,S.Roopa, and H.L.Parashivmurthy, Topological indices of Vitamin D3,International Journal of Engineering and Technology,7(4) (2018) 6276-6284.
[4] P.Sarkar, and A.Pal, General fifth Zagreb polynomials of Benzene ring implanted in the P-type surface in 2D network, Biointerface research in Applied Chemistry,10(6) (2020) 6881-6892.
[5] E.Deutsch and S.Klavzar, M-polynomials and degree-based topological indices, Iranian Journal of Mathematical Chemistry, 6(2) (2015) 93-102.
[6] H.M.A.Siddique, and M.Imran,Computing the metric dimension of wheel related graphs, Applied Mathematics and Computation, 242 (2014) 624-632.
[7] N.K.Raut and G.K.Sanap, International Journal of Innovative Science, Engineering and Technology, 6(9) (2019) 477-484.
[8] V.R.Kulli, Computation of Multiplicative (a,b)-Status index of certain graphs, Journal of Mathematics and Information, 18 (2020) 50-55.
[9] M.U.Butt, Some degree-based topological indices of wheel related graphs, M.S.Thesis in Mathematics, COMSATS University Islamabad, Spring (2019).
[10] M.Cancan,M.Hussain, and H.Ahmad, Distance and eccentricity based polynomials and topological indices of m-level wheel graph,Proyecciones,39(4) (2020) 869-885.
[11] R.H.Khan,A.Q.Baig,R.Kiran,I.Haider,M.Rizawn, and A.Elahi, M-polynomial and degree-based topological indices of Dexamethasome,Chloroquine and Hydroxychloroquine;using in COVID-19,International Journal of Scientific Engineering and Science 4(7) (2020) 47-52.
[12] P.J.N.Thayamathy,P.Elango, and M.Koneswaran, International Research Journal of Pure and Applied Chemistry,16(4) (2018) 1-9.
[13] J.B.Liu,M.Younas,M.Habib, and M.Yousaf, M-polynomials and degree-based topological indices of VC5C7[p,q] and HC5C7[p,q] nanotubes ,IEEE Access.7 (2019) 41125-41132.
[14] M.Riaz,W.Gao, and A.Q.Baig, M-polynomials and degree-based topological indices of some families of convex polytopes, Open J.Math.Science,2(1) (2018) 18-28.
[15] W.Gao, M.Younas, A.Farooq,A.Mahboob, and W.Nazeer, M-polynomials and degree-based topological indices of the crystallographic structure of molecules, Biomolecues, MDPI, (2018) 1-18.
[16] M.Munir,W.Nazeer,S.Rafique,A.R.Nizami, and S.M.Kang,. M-polynomial and degree-based topological indices of Titania nanotubes, Symmetry, 8(11)(2016) 117.
[17] A.Ali,W.Nazeeer,M.Munir,and S.M.Kang, M-polynomials and topological indices of zigzag and rhombic benzenoid systems,Open Journal of Chemistry,16,No.1,(2018) 73-78.
[18] M.Munir,W.Nazeer,S.Rafique,S.M.Kang,M-polynomial and degree-based topological indices of polyhex nanotubes,Symmetry,8(18) (2016) 149.
[19] X.Zhau,M.Habib,A.Hanif, and A.Ye, Topological invariants for the line graphs of some classes of graphs, Open Chem.,17 (2019) 1483-1490.
[20] S.Das, and S.Rai, M-polynomial and related degree-based topological indices of the third type of hex-derived network, Nanosystems Physics, Chemistry, Mathematics, 11-3, (2020) 264-274.
[21] Y.C.Kwun,A.Ali,W.Nazeer,M.A.Chaudhary,and S.M.Kang, Hindawi, Journal of Chemistry, (2018) 108.
[22] E.Deutsch, and O.S.Klavzar, M. polynomial and degree-based topological indices, arXiv, 1407.1592 v1 [math.CO], (2014) 01-10.
[23] M.Javaid, and C.Y.Jung, M-polynomials and topological indices of Silicate and oxide networks, International Journal of Pure and Applied Mathematics,115(1) (2017) 129-152.
[24] I.Gutman,and J.Tosovic,Testing quality of molecular structure descriptors, vertex degree-based topological indices, Journal Serb.Chem.78(6) (2013) 805-810.
[25] R.Todeschini,and V.Consonni, Handbook of Molecular Descriptors,Wiley-VCH,Weinheim,(2000).
[26] N.Trinajstic, Chemical Graph Theory, CRC Press, Boca Raton, F.,(1992).
[27] J.A.Bondy, U.S.R.Murthy, Graph Theory with Applications, Macmillan London and Elsevier, New York,(1976).
[28] N.Deo, Graph Theory, Prentice-Hall of India ,Private Ltd. New Delhi, (2007) 01-11.
[29] D.B.West, Introduction to Graph Theory, second edition, PHI Learning Private Ltd. New Delhi,(2009) 67-80.
N.K. Raut, "Topological Indices and M-Polynomials of Wheel And Gear Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 67, no. 8, pp. 26-37, 2021. Crossref, https://doi.org/10.14445/22315373/IJMTT-V67I8P503