Study of topology of block shift networks via topological indices

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-04-0055

Keywords:

Topological index, Physical properties of compounds, Graph, Network

Abstract

Topological indices(TIs) are important numerical number associate with the molecular graph of a chemical structure/compound because due to these parameters, one can guess almost all properties of concerned structure/compound with our performing experiments. In recent years, huge amount work has been done for calculating degreedependent indices for different structures/compouds. In order to compute TIs, one need to do many calculations. Our aim of this paper is to present a simple method to compute degree-dependent TIs. We computed M-polynomials for Block Shift Networks and with the help of this simple algebraic polynomials, we recovered nine important TIs for Block Shift Networks. Our work is important for chemists, physicians and pharmaceutical industry.

Author Biographies

Murat Cancan, Van Yznc Yil University.

Faculty of Education.

Iftikhar Ahmad, COMSATS University Islamabad.

Dept. of Mathematics, Lahore.

Sarfarz Ahmad, COMSATS University Islamabad.

Dept. of Mathematics.

References

M. S. Anjum and M. U. Safdar, “K Banhatti and K hyper-Banhatti indices of nanotubes”, Engineering and applied science letters, vol. 2, no. 1, pp. 19–37, Mar. 2019, doi: 10.30538/psrp-easl2019.0013

A. T. Balaban, “Highly discriminating distance-based topological index”, Chemical physics letters, vol. 89, no. 5, pp. 399–404, Jul. 1982, doi: 10.1016/0009-2614(82)80009-2

G. Caporossi, I. Gutman, P. Hansen, and L. Pavlovi?, “Graphs with maximum connectivity index”, Computational biology and chemistry, vol. 27, no. 1, pp. 85–90, Feb. 2003, doi: 10.1016/S0097-8485(02)00016-5

N. De, “Hyper Zagreb index of bridge and Chain graphs”, Open journal of mathematical sciences, pp. 1–17, 2018, doi: 10.30538/oms2018.0013

E. Deutsch and Klavžar, “S. M-Polynomial, and degree-based topological indices”, Iranian journal of mathematical chemistry, vol. 6, no. 2, pp. 93-102, 2015, doi: 10.22052/IJMC.2015.10106

O. Favaron, M. Mahéo, and J.-F. Saclé, “Some eigenvalue properties in graphs (conjectures of Graffiti — II)”, Discrete mathematics, vol. 111, no. 1-3, pp. 197–220, Feb. 1993, doi: 10.1016/0012-365X(93)90156-N

B. Furtula, A. Graovac, and D. Vuki?evi?, “Augmented Zagreb index”, Journal of mathematical chemistry, vol. 48, no. 2, pp. 370–380, Apr. 2010, doi: 10.1007/s10910-010-9677-3

W. Gao, W. Wang, D. Dimitrov, and Y. Wang, “Nano properties analysis via fourth multiplicative ABC indicator calculating”, Arabian journal of chemistry, vol. 11, no. 6, pp. 793–801, Sep. 2018, doi: 10.1016/j.arabjc.2017.12.024

W. Gao, W. Wang, and M. R. Farahani, “Topological indices study of molecular structure in anticancer drugs”, Journal of chemistry, vol. 2016, Art ID. 3216327, 2016, doi: 10.1155/2016/3216327

M. Ghorbani and N. Azimi, “Notes on mulyiple Zagreb indices”, Iranian journal of mathematical chemistry, vol. 3, no. 2, pp. 137-143, 2012, doi: 10.22052/IJMC.2012.5233

C. K. Gupta, V. Lokesha, S. B. Shwetha, and P. S. Ranjini, “On the symmetric division deg index of graph”, Southeast asian bulletin of mathematics, vol. 40, no. 1, pp. 59-80, 2016. [On line]. Available: https://bit.ly/2Ck4tKF

I. Gutman and K. C. Das, “The first Zagreb indices 30 years after”, MATCH communications in mathematical and in computer chemistry, vol. 50, pp. 83-92, 2004. [On line]. Available: https://bit.ly/3ea6XJF

G. Liu, Z. Jia, and W. Gao, “Ontology similarity computing based on stochastic primal dual coordinate technique,” Open Journal of Mathematical Sciences, vol. 2, no. 1, pp. 221–227, Aug. 2018, doi: 10.30538/oms2018.0030

J.-B. Liu and X.-F. Pan, “Minimizing Kirchhoff index among graphs with a given vertex bipartiteness”, Applied mathematics and computation, vol. 291, pp. 84–88, Dec. 2016, doi: 10.1016/j.amc.2016.06.017

J.-B. Liu, X.-F. Pan, F.-T. Hu, and F.-F. Hu, “Asymptotic Laplacian-energy-like invariant of lattices”, Applied mathematics and computation, vol. 253, pp. 205–214, Feb. 2015, doi: 10.1016/j.amc.2014.12.035

J.-B. Liu, C. Wang, S. Wang, and B. Wei, “Zagreb indices and multiplicative Zagreb indices of Eulerian graphs”, Bulletin of the Malaysian Mathematical Sciences Society, vol. 42, no. 1, pp. 67–78, Feb. 2017, doi: 10.1007/s40840-017-0463-2

J.-B. Liu, J. Zhao, and Z. Zhu, “On the number of spanning trees and normalized Laplacian of linear octagonal?quadrilateral networks”, International journal of quantum chemistry, vol. 119, no. 17, pp. Art ID. e25971, 2019, doi: 10.1002/qua.25971

A. Mili?evi?, S. Nikoli?, and N. Trinajsti?, “On reformulated Zagreb indices,” Molecular diversity, vol. 8, no. 4, pp. 393–399, Dec. 2004, doi: 10.1023/B:MODI.0000047504.14261.2a

M. Munir, W. Nazeer, S. Rafique, and S. Kang, “M-Polynomial and related topological indices of nanostar dendrimers”, Symmetry, vol. 8, no. 9, Art ID. 97, Sep. 2016, doi: 10.3390/sym8090097

M. Munir, W. Nazeer, S. Rafique, and S. Kang, “M-Polynomial and degree-based topological indices of polyhex nanotubes”, Symmetry, vol. 8, no. 12, Art ID. 149, Dec. 2016, doi: 10.3390/sym8120149

M. Munir, W. Nazeer, S. Rafique, A. R. Nizami, and S. M. Kang, “Some computational aspects of triangular boron nanotube”, Symmetry, vol. 9, no. 1, Art ID. 6, Jan. 2016, doi: 10.3390/sym9010006

M. Munir, W. Nazeer, Z. Shahzadi, and S. Kang, “Some invariants of circulant graphs”, Symmetry, vol. 8, no. 11, pp. Art ID. 134, Nov. 2016, doi: 10.3390/sym8110134

S. Noreen and A. Mahmood, “Zagreb polynomials and redefined Zagreb indices for the line graph of carbon nanocones”, Open journal of mathematical analysis, vol. 2, no. 1, pp. 66–73, Jun. 2018., doi: 10.30538/psrp-oma2018.0012

M. Randi?, “Characterization of molecular branching”, Journal of the American Chemical Society, vol. 97, no. 23, pp. 6609–6615, Nov. 1975, doi: 10.1021/ja00856a001

H. M. U. Rehman, R. Sardar, and A. Raza, “Computing topological indices of Hex Board and its line graph”, Open journal of mathematical sciences, vol. 1, no. 1, pp. 62–71, 2017, doi: 10.30538/oms2017.0007

M. Riaz, W. Gao, and A. Q. Baig, “M-Polynomials and degree-based topological indices of some families of convex polytopes”, Open journal of mathematical sciences, vol. 2, no. 1, pp. 18–28, Feb. 2018, doi: 10.30538/oms2018.0014

M. S. Sardar, S. Zafar, and M. R. Farahani, “The generalized Zagreb index of Capra-designed planar benzenoid series Cak(C6),” Open journal of mathematical sciences, vol. 1, no. 1, pp. 44–51, 2017, doi: 10.30538/oms2017.0005

H. Siddiqui and M. R. Farahani, “Forgotten polynomial and forgotten index of certain interconnection networks”, Open journal of mathematical analysis, vol. 1, no. 1, pp. 44–59, Dec. 2017, doi: 10.30538/psrp-oma2017.0005

H. Wiener, “Structural determination of paraffin boiling points”, Journal of the American Chemical Society, vol. 69, no. 1, pp. 17–20, Jan. 1947, doi: 10.1021/ja01193a005

L. Yan, M. R. Farahani, and W. Gao, “Distance-based Indices computation of symmetry molecular structures”, Open journal of mathematical sciences, vol. 2, no. 1, pp. 323–337, Nov. 2018, doi: 10.30538/oms2018.0038

Published

2020-07-28

How to Cite

[1]
M. Cancan, I. Ahmad, and S. Ahmad, “Study of topology of block shift networks via topological indices”, Proyecciones (Antofagasta, On line), vol. 39, no. 4, pp. 887-902, Jul. 2020.

Most read articles by the same author(s)