\(M\)-Polynomial and topological indices of Hanoi graph and generalized wheel graph

Downloads

DOI:

https://doi.org/10.26637/MJM0804/0140

Abstract

There are plenty of topological indices used in chemistry to study the chemical behavior and physical properties of molecular graphs. In the literature, several results are computed for degree based topological indices like “first Zagreb index, second Zagreb index, modified second Zagreb index, generalized Randi´c index, inverse Randi´c index, symmetric sum division index, harmonic index, inverse sum index, augmented Zagreb index”. In this paper, we have investigated the aforesaid degree based topological indices for Hanoi graph and generalized wheel graph with the help of M-polynomial.

Keywords:

Topological indices, M-polynomial, Hanoi graph \( H_n\), generalized wheel graph \(W_n^m\)

Mathematics Subject Classification:

Mathematics
  • Ravi Ratn Gaur Department of Mathematics, University of Rajasthan, Jaipur-302004, India.
  • Pravin Garg Department of Mathematics, University of Rajasthan, Jaipur-302004, India.
  • Bharat Kumar Yadav Department of Mathematics, Mohan Lal Sukhadia University, Udaipur-323001, India.
  • Pages: 2149-2157
  • Date Published: 01-10-2020
  • Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

A.T. Balaban, I. Motoc, D. Bonchev and O. Mekenyan, "Topological indices for structure-activity correlations", Topics in Current Chemestry, 114(1983), 21-55.

I. Gutman, "Degree based topological indices", CroaticaChemica Acta, 86(4)(2013), 351-361.

Y.C. Kwun, A. Ali and W. Nazeer, "M-polynomials and degree-based topological indices of triangular, hourglass and jagged-rectangle benzenoid systems", Journal of Chemistry, (2018), Art-ID 8213950.

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

M. Munir, W. Nazeer, S. Rafique and S.M. Kang, " $M$ polynomial and related topological indices of nanostar dendrimers", Symmetry, 8(9)(2016), 97.

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.

I. Gutman and N. Trinajstić, "Graph theory and molecular orbitals. total $pi$-electron energy of alternant hydrocarbons", Chemical Physics Letters, 17(1972), 535-538.

I. Gutman, B. Rušcič, N. Trinajstić and C.F. Wilcox, "Graph theory and molecular orbitals.XII. acyclic polyenes", Chemical Physics, 62(1975), 3399-3405.

B. Borovicanin, K.C. Das, B. Furtula and I. Gutman, "Bounds for Zagreb indices", MATCH Communications in Mathematical and in Computer Chemistry, 78(2017), 17-100.

E. Milovanovića, I. Milovanovića and M. Jamilb, "Some properties of the Zagreb indices", FILOMAT, Faculty of Sciences and Mathematics, University of Nis̆, Serbia, 32(7)(2018), 2667-2675.

S. Nikolić, G. Kovačević, A. Miličević and N. Trinajstić,"The Zagreb indices 30 years after", CroaticaChemica Acta, 76(2003), 113-124.

E. Estrada, L. Torres, L. Rodríguez and I. Gutman, "An atom bond connectivity index", Indian Journal of Chemistry, 37A(1998), 849-855.

B. Furtula, A. Graovac and D. Vukičević, "Augmented Zagreb index", Mathematical Chemistry, 48(2010), 370380.

M. Randić, "On characterization of molecular branching", Journal of the American Chemical Society, 97(1975), 6609-6615.

B. Bollobás and P. Erdös, "Graphs of extremal weights", Ars Combinatoria, 50(1998), 225-233.

D. Amić, D. Belo, B. Lucić, S. Nikolic and N. Trinajstic, "The vertex-connectivity index revisited", Journal of Chemical Information & Computer Sciences, 38(5)(1998), 819822.

X. Li and I. Gutman, "Mathematical aspects of Randictype molecular structure descriptors", Faculty of Science, University of Kragujevac, Kragujevac, (2006).

S. Fajtlowicz, "On conjectures on graffiti-II", CongressusNumerantium, 60(1987), 187-197.

O. Favaron, M. Mahéo and J.F. Saclé, "Some eigenvalue properties in graphs(conjectures of graffiti II)", Discrete Mathematics, 111(1993), 197-220.

L. Zhong, "The harmonic index on graphs", Applied Mathematics Letters, 25(2012), 561-566.

J. Sedlar, D. Stevanović and A. Vasilyev, "On the inverse sum indeg index", Discrete Applied Mathematics, 184(2015), 202-212.

D. Vukicevic, "Bond additive modeling 2 mathematical properties of max-min rodeg index", CroaticaChemica Acta, 54(2010), 261-273.

  • NA

Metrics

Metrics Loading ...

Published

01-10-2020

How to Cite

Ravi Ratn Gaur, Pravin Garg, and Bharat Kumar Yadav. “\(M\)-Polynomial and Topological Indices of Hanoi Graph and Generalized Wheel Graph”. Malaya Journal of Matematik, vol. 8, no. 04, Oct. 2020, pp. 2149-57, doi:10.26637/MJM0804/0140.