Computation of topological indices of linear chains of perylene and coronene using M-polynomial

Ashwini Shivappa  Yalnaik; Mookanahallipatna Shivanna  Ranganath; Veerabhadraiah  Lokesha; Raju Basavaraju  Jummannaver

doi:10.59400/jam.v2i3.563

Computation of topological indices of linear chains of perylene and coronene using M-polynomial

Ashwini Shivappa Yalnaik Department of Studies in Mathematics, Davangere University, Davangere 577007, India
Mookanahallipatna Shivanna Ranganath Department of Studies in Mathematics, Davangere University, Davangere 577007, India
Veerabhadraiah Lokesha Department of Studies in Mathematics, Vijayanagara Sri Krishnadevarya University, Ballari 583105, India
Raju Basavaraju Jummannaver P. G. Department of Mathematics, Karnatak Science College, Dharwad 580001, India

Article ID: 563

1267 Views, 1211 PDF Downloads

DOI: https://doi.org/10.59400/jam.v2i3.563

Keywords: topological indices; graph polynomials; subdivision graph; semi-total point graph

Abstract

The M-polynomial yields degree based topological indices that anticipate different physical and chemical properties of material being scrutinized. In this work, M-polynomial of linear chains of perylene and coronene are acquired. From M-polynomial, some degree based topological dicriptors are determined. Some topological indices of these compounds are compared by plotting graphs.

References

[1]Hassani F, Iranmanesh A, Mirzaie S. Schultz and modified Schultz polynomials of C100 fullerene. MATCH Commun. Math. Comput. Chem. 2013; 69: 87-92.

[2]Sourav M, Muhammad I, Nilanjan D, et al. Neighborhood M-polynomial of titanium compounds. Arabian Journal of Chemistry. 2021; 14(8): 103244.

[3]Lokesha V, Kulli VR, Jain S, et al. Certain topological indices and related polynomials for polysaccharides. TWMS Journal of Applied and Engineering Mathematics. 2023; 13(3): 990-997.

[4]Deutsch E, Klavžar S. M-polynomial and degree-based topological indices. arXiv Preprint 2014; arXiv:1407.1592.

[5]Shanthakumari Y, Lokesha V, Manjunath M. Invariant Polynomials of N-Coronene. Journal of International Academy of Physical Sciences. 2021; 25(2): 231-242.

[6]Lokesha V, Shruti R, Sinan Cevik A. M-Polynomial of Subdivision and complementary Graphs of Banana Tree. Graph.J. Int. Math. Virtual Inst. 2020; 10(1): 157-182.

[7]Kumar DS, Ranjini PS, Lokesha V. Investigation on some topological indices of carbon nanobud through M-polynomial. Proceedings of the Jangjeon Mathematical Society. 2022; 25: 4.

[8]Bindusree AR, Lokesha V, Ranjini PS. ABC index on subdivision graphs and line graphs. International Organization of Scientific Research Journal of Mathematics (IOSRJM). 2014; 01-06.

[9]Lokesha V, Shruti R, Sinan Cevik A. On certain topological indices of nanostructures usingq (g) and r (g) operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics. 2018; 67(2): 178-187.

[10]Gutman I, Ch Das K. The first Zagreb index 30 years after. MATCH Commun. Math. Comput. Chem. 2004; 50(1): 83-92.

[11]Miličević A, Nikolić S, Trinajstić N. On reformulated Zagreb indices. Molecular Diversity. 2004; 8(4): 393-399.

[12]Amić D, Bešlo D, Lucić B, et al. The vertex-connectivity index revisited. Journal of Chemical Information and Computer Sciences. 1998; 38(5): 819-822.

[13]Bollobás B, Erdös P. Graphs of extremal weights. Ars Combinatoria. 1998; 50: 225.

[14]Gupta CK, Lokesha V, Shwetha SB, et al. On the Symmetric Division deg Index of Graph. Southeast Asian Bulletin of Mathematics. 2016; 40(1).

[15]Shwetha Shetty B, Lokesha V. , Ranjini PS. On the harmonic index of graph operations. Transactions on Combinatorics. 2015; 4(4): 5-14.

[16]Vukičević, Gašperov M. Bond additive modeling 1. Adriatic indices. Croatica Chemica Acta. 2010; 83(3): 243-260.

[17]Ramane HS, Yalnaik AS. Bounds for the status connectivity index of Line graphs. International Journal of Computational and Applied Mathematics. 2017; 12: 3.

[18]Ramane HS, Jummannaver RB, Sedghi S, et al. Some degree based topological indices of generalized transformation graphs and of their complements. Int. J. Pure Appl. Math. 2016; 109(3): 493-509.

Published

2024-06-25

How to Cite

Yalnaik, A. S., Ranganath, M. S., Lokesha, V., & Jummannaver, R. B. (2024). Computation of topological indices of linear chains of perylene and coronene using M-polynomial. Journal of AppliedMath, 2(3), 563. https://doi.org/10.59400/jam.v2i3.563

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