# Redefined Zagreb indices of Rhombic, triangular, Hourglass and Jagged-rectangle benzenoid systems

## DOI:

https://doi.org/10.22199/issn.0717-6279-2020-04-0053## Keywords:

Topological index, Zagreb index, Benzenoid system## Abstract

*In the fields of mathematical chemistry and chemical graph theory, a topological index generally called a connectivity index is a kind of a molecular descriptor that is calculated in perspective of the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which depict its topology and are graph invariant up to graph isomorphism. Topological indices are used for example in the progression of quantitative structure-activity relationships (QSARs) in which the common activity or distinctive properties of atoms are connected with their molecular structure. There are in excess of 140 topological indices but none of them totally describe the molecular compound completely so there is dependably a space to characterize and register new topological indices. Benzenoid Systems are utilized basically as an intermediate to make different synthetic compounds. In this report we aim to compute redefined Zagreb indices for Zigzag, Rhombic, triangular, Hourglass and Jagged-rectangle Benzenoid systems.*

## References

S. Ahmad, H. M. A. Siddiqui, A. Ali, M. R. Farahani, M. Imran, and I. N. Cangul, “On Wiener index and Wiener polarity index of some polyomino chains”, Journal of discrete mathematical sciences and cryptography, vol. 22, no. 7, pp. 1151–1164, 2019, doi: 10.1080/09720529.2019.1688965

A. Ali, W. Nazeer, M. Munir, and S. M. Kang, “M-polynomials and topological indices of zigzag and rhombic Benzenoid systems”, Open chemistry, vol. 16, no. 1, pp. 73–78, Jan. 2018, doi: 10.1515/chem-2018-0010.

U. Ali, Y. Ahmad, and M. S. Sardar, “On 3-total edge product cordial labeling of tadpole, book and flower graphs”, Open journal of mathematical sciences, vol. 4, no. 1, pp. 48–55, 2020, doi: 10.30538/oms2020.0093

F. Asif, Z. Zahid, and S. Zafar, “Leap Zagreb and leap hyper-Zagreb indices of Jahangir and Jahangir derived graphs”, Engineering and Applied Science Letter, vol. 3, no. 2, pp. 1-8, 2020. [On line]. Available: https://bit.ly/3dm05rH

A. T. Balaban, I. Motoc, D. Bonchev, and O. Mekenyan, “Topological indices for structure-activity correlations”, in Topics in current chemistry. Steric effects in drug design, vol. 114, Berlin: Springer, 1983, pp. 21–55.

M. Cancan, S. Ediz, and M. R. Farahani, “On ve-degree atom-bond connectivity, sum-connectivity, geometric-arithmetic and harmonic indices of copper oxide”, Eurasian chemical communications, vol. 2, no. 5, pp. 641–645, 2020, doi: 10.33945/SAMI/ECC.2020.5.11

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

W. Gao and M. R. Farahani, “The hyper-zagreb index for an infinite family of nanostar dendrimer”, Journal of discrete mathematical sciences and cryptography, vol. 20, no. 2, pp. 515–523, 2017, doi: 10.1080/09720529.2016.1220088

W. Gao and M. R. Farahani, “The zagreb topological indices for a type of benzenoid systems jagged-rectangle”, Journal of interdisciplinary mathematics, vol. 20, no. 5, pp. 1341–1348, 2017, doi: 10.1080/09720502.2016.1232037

W. Gao, L. Shi, and M. R. Farahani, “Szeged Related Indices of TUAC6[p, q]”, Journal of discrete mathematical sciences and cryptography, vol. 20, no. 2, pp. 553–563, 2017, doi: 10.1080/09720529.2016.1228312

W. Gao, M. Younas, A. Farooq, A. Virk, and W. Nazeer, “Some reverse degree-based topological indices and polynomials of dendrimers”, Mathematics, vol. 6, no. 10, Art ID. 214, Oct. 2018, doi: 10.3390/math6100214

I. Gutman, B. Rucić, N. Trinajstić, and C. F. Wilcox Jr. “Graph theory and molecular orbitals. XII. Acyclic polyenes”, The journal of chemical physics, vol. 62, no. 9, Art ID. 3399, May 1975, doi: 10.1063/1.430994

I. Gutman and N. Trinajstić, “Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons”, Chemical physics letters, vol. 17, no. 4, pp. 535–538, Dec. 1972, doi: 10.1016/0009-2614(72)85099-1

Y. Huang, B. Liu and L. Gan, “Augmented zagreb index of connected graphs”, MATCH communication in mathematical and in computer chemistry, vol. 67, no. 2, pp. 483-494, 2012. [On line]. Available: https://bit.ly/2NdkHYe

Y. C. Kwun, A. Ali, W. Nazeer, M. A. Chaudhary, and S. M. Kang, “M-polynomials and degree-based topological indices of triangular, Hourglass, and Jagged-Rectangle Benzenoid systems”, Journal of chemistry, vol. 2018, Art ID. 8213950, Dec. 2018, doi: 10.1155/2018/8213950

J.-B. Liu, M. Younas, M. Habib, M. Yousaf, and W. Nazeer, “M-polynomials and degree-based topological indices of VC5C7[p,q] and HC5C7[p,q] Nanotubes”, IEEE access, vol. 7, pp. 41125–41132, Mar. 2019, doi: 10.1109/ACCESS.2019.2907667

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, 2016, doi: 10.3390/sym8120149

P. S. Ranjini, V. Lokesha, and A. Usha, “Relation between phenylene and hexagonal squeeze using harmonic index”, International journal of graph theory; vol. 1, pp-116-121, 2013

A. Shah and S. A. U. H. Bokhary, “On chromatic polynomial of certain families of dendrimer graphs”, Open journal of mathematical sciences, vol. 3, no. 1, pp. 404–416, 2019, doi: 10.30538/oms2019.0083

A. Tabassum, M. A. Umar, M. Perveen, and A. Raheem, “Antimagicness of subdivided fans”, Open journal of mathematical sciences, vol. 4, no. 1, pp. 18–22, 2020, doi: 10.30538/oms2020.0089

M. A. Umar, N. Ali, A. Tabassum, and B. R. Ali, “Book graphs are cycle antimagic”, Open journal of mathematical sciences, vol. 3, no. 1, pp. 184–190, 2019, doi: 10.30538/oms2019.0061

## Published

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*Proyecciones (Antofagasta, On line)*, vol. 39, no. 4, pp. 851-867, Jul. 2020.

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Copyright (c) 2020 Mohanad A. Mohammed, Raad Haoer, Ashaq Ali, Maqbool Ahmad, Mohammad Reza Farahani, Saima Nazeer

This work is licensed under a Creative Commons Attribution 4.0 International License.