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Current Organic Synthesis

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ISSN (Print): 1570-1794
ISSN (Online): 1875-6271

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Research Article

Forgotten Topological and Wiener Indices of Prime Ideal Sum Graph of ℤn

Author(s): Esra Öztürk Sözen, Elif Eryaşar and Cihat Abdioğlu*

Volume 21, Issue 3, 2024

Published on: 01 August, 2023

Page: [239 - 245] Pages: 7

DOI: 10.2174/1570179420666230606140448

Price: $65

Abstract

Background: Chemical graph theory is a sub-branch of mathematical chemistry, assuming each atom of a molecule is a vertex and each bond between atoms as an edge.

Objective: Owing to this theory, it is possible to avoid the difficulties of chemical analysis because many of the chemical properties of molecules can be determined and analyzed via topological indices. Due to these parameters, it is possible to determine the physicochemical properties, biological activities, environmental behaviours and spectral properties of molecules. Nowadays, studies on the zero divisor graph of ℤn via topological indices is a trending field in spectral graph theory.

Methods: For a commutative ring R with identity, the prime ideal sum graph of R is a graph whose vertices are nonzero proper ideals of R and two distinctvertices I and J are adjacent if and only if I + J is a prime ideal of R.

Results: In this study the forgotten topological index and Wiener index of the prime ideal sum graph of ℤn are calculated for n=pα ,pq, p2q, p2q2, pqr, p3q, p2qr, pqrs where p, q, r and s are distinct primes and a Sage math code is developed for designing graph and computing the indices.

Conclusion: In the light of this study, it is possible to handle the other topological descriptors for computing and developing new algorithms for next studies and to study some spectrum and graph energies of certain finite rings with respect to PIS-graph easily.

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Graphical Abstract

[1]
Çolakoğlu, Ö. QSPR modelling with topological indices of some potential drug candidates against covid-19. J. Math., 2022, 2022, 1-9.
[http://dx.doi.org/10.1155/2022/3785932]
[2]
Gürsoy, A.; Gürsoy, N.K.; Ülker, A. Computing forgotten topological index of zero-divisor graphs of commutative rings. Turk. J. Math., 2022, 46(5), 1845-1863.
[http://dx.doi.org/10.55730/1300-0098.3236]
[3]
Gürsoy, A.; Ülker, A.; Kırcalı Gürsoy, N. Sombor index of zero divisor graphs of commutative rings. An. St. Univ. Ovidius Constanta, 2022, 30(2), 231-257.
[http://dx.doi.org/10.2478/auom-2022-0028]
[4]
Estrada, E.; Bonchev, D. Chemical graph theory. In: Hand book of Graph Theory; , 2013. Available from: http://www.crcpress.com/product/isbn/9781439880180
[5]
Gutman, I. Degree-based topological indices. Croat. Chem. Acta, 2013, 86(4), 351-361.
[http://dx.doi.org/10.5562/cca2294]
[6]
Asir, T.; Rabikka, V. The Wiener index of the zero-divisor graph of Z n. Discrete Appl. Math., 2022, 319, 461-471.
[http://dx.doi.org/10.1016/j.dam.2021.02.035]
[7]
Furtula, B.; Gutman, I. A forgotten topological index. J. Math. Chem., 2015, 53(4), 1184-1190.
[http://dx.doi.org/10.1007/s10910-015-0480-z]
[8]
Gao, W.; Farahani, M.R.; Shi, L. Forgotten topological index of some drug structures. Acta Med., 2016, 32(1), 579-585.
[9]
Ye, Y.; Chen, H.; Zou, Y.; Zhao, H. Study on self-healing and corrosion resistance behaviors of functionalized carbon dot-intercalated graphene-based waterborne epoxy coating. J. Mater. Sci. Technol., 2021, 67, 226-236.
[http://dx.doi.org/10.1016/j.jmst.2020.06.023]
[10]
Ye, Y.; Chen, H.; Zou, Y.; Ye, Y.; Zhao, H. Corrosion protective mechanism of smart graphene-based self-healing coating on carbon steel. Corros. Sci., 2020, 174, 108825.
[http://dx.doi.org/10.1016/j.corsci.2020.108825]
[11]
Ramane, H.S.; Jummannaver, R.B. Note on forgotten topological index of chemical structure in drugs. Applied Mathematics and Nonlinear Sciences, 2016, 1(2), 369-374.
[http://dx.doi.org/10.21042/AMNS.2016.2.00032]
[12]
Gao, W.; Siddiqui, M.K.; Imran, M.; Jamil, M.K.; Farahani, M.R. Forgotten topological index of chemical structure in drugs. Saudi Pharm. J., 2016, 24(3), 258-264.
[http://dx.doi.org/10.1016/j.jsps.2016.04.012] [PMID: 27275112]
[13]
Anderson, D.F.; Livingston, P.S. The zero divisor graph of a commutative ring. J. Algebra, 1999, 217(2), 434-447.
[http://dx.doi.org/10.1006/jabr.1998.7840]
[14]
Beck, I. Coloring of commutative rings. J. Algebra, 1988, 116(1), 208-226.
[http://dx.doi.org/10.1016/0021-8693(88)90202-5]
[15]
Singh, P.; Bhat, V.K. Adjacency matrix and Wiener index of zero dividor graph Γ(Z_n ). J. App. Math. Comput., 2020.
[http://dx.doi.org/10.1007/s12190-020-01460-2]
[16]
Kırcalı Gürsoy, N.; Ülker, A.; Gürsoy, A. Independent domination polynomial of zero-divisor graphs of commutative rings. Soft Comput., 2022, 26(15), 6989-6997.
[http://dx.doi.org/10.1007/s00500-022-07217-2]
[17]
Rather, B.A.; Ali, F.; Alsaeed, S.; Naeem, M. Hosoya Polynomials of power graphs of certain finite groups. Molecules, 2022, 27(18), 6081.
[http://dx.doi.org/10.3390/molecules27186081] [PMID: 36144814]
[18]
Banerjee, S. Laplacian spectrum of comaximal graph of the ring ℤn. Spec. Matrices, 2022, 10(1), 285-298.
[http://dx.doi.org/10.1515/spma-2022-0163]
[19]
Nath, R.; Rajat, K.N.; Sharafdini, R. Various spectra and energies of commuting graphs of finite rings. Hacet. J. Math. Stat., 2020, 49(6), 1-11.
[http://dx.doi.org/10.15672/hujms.540309]
[20]
Saha, M.; Das, A.; Çelikel, E.Y.; Abdioğlu, C. Prime ideal sum graph of a commutative ring. J. Algebra its Appl., 2022, 2350121.
[http://dx.doi.org/10.1142/S0219498823501219]

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