Algorithms for Distance-based Topological Indices for Zero Divisor Graphs of Commutative Rings with Primes
Main Article Content
Abstract
Abstract
Mathematical solutions are sometimes complex to solve mathematically. Algorithms can provide the solution to these problems. Our article introduced algorithms to compute distance-based topological indices for zero divisor graphs containing finite rings as Zp1p2 × Zq. and Zp2 × Zq, having primes p1, p2, and q. Algorithm results can be reused in standing physical structures, solving computer network problems, and designing mechanics.
Downloads
Article Details
Copyright (c) 2024 Elahi K.
This work is licensed under a Creative Commons Attribution 4.0 International License.
Licensing and protecting the author rights is the central aim and core of the publishing business. Peertechz dedicates itself in making it easier for people to share and build upon the work of others while maintaining consistency with the rules of copyright. Peertechz licensing terms are formulated to facilitate reuse of the manuscripts published in journals to take maximum advantage of Open Access publication and for the purpose of disseminating knowledge.
We support 'libre' open access, which defines Open Access in true terms as free of charge online access along with usage rights. The usage rights are granted through the use of specific Creative Commons license.
Peertechz accomplice with- [CC BY 4.0]
Explanation
'CC' stands for Creative Commons license. 'BY' symbolizes that users have provided attribution to the creator that the published manuscripts can be used or shared. This license allows for redistribution, commercial and non-commercial, as long as it is passed along unchanged and in whole, with credit to the author.
Please take in notification that Creative Commons user licenses are non-revocable. We recommend authors to check if their funding body requires a specific license.
With this license, the authors are allowed that after publishing with Peertechz, they can share their research by posting a free draft copy of their article to any repository or website.
'CC BY' license observance:
|
License Name |
Permission to read and download |
Permission to display in a repository |
Permission to translate |
Commercial uses of manuscript |
|
CC BY 4.0 |
Yes |
Yes |
Yes |
Yes |
The authors please note that Creative Commons license is focused on making creative works available for discovery and reuse. Creative Commons licenses provide an alternative to standard copyrights, allowing authors to specify ways that their works can be used without having to grant permission for each individual request. Others who want to reserve all of their rights under copyright law should not use CC licenses.
Gutman I. Selected properties of the Wiener polynomials. Graph Theory Notes New York. 1993;25:13-18.
Dobrynin AA, Entringer R, Gutman I. Wiener index of trees: theory and applications. Acta Appl Math. 2001;66:211–249. Available from: https://link.springer.com/article/10.1023/a:1010767517079
Wiener H. Structural determination of paraffin boiling points. J Am Chem Soc. 1947;69:17-20. Available from: https://pubs.acs.org/doi/pdf/10.1021/ja01193a005
Ba˘ca M, Horvrathova J, Mokriˇsova M, Suhanyiov`a A. On topological indices of fullerenes. Appl Math Comput. 2015;251:154–161. Available from: https://doi.org/10.1016/j.amc.2014.11.069
Baig AQ, Imran M, Ali H, Rehman SU. Computing topological polynomial of certain nanostructures. J Optoelectron Adv Mater. 2015;17(5-6):877–883. Available from: https://www.researchgate.net/publication/279749117_Computing_topological_polynomials_of_certain_nanostructures
Basak SC, Magnuson VR, Niemi GJ, Regal RR, Veith GD. Topological indices: their nature, mutual relatedness, and applications. Math Modell. 1987;8:300-305. Available from: https://doi.org/10.1016/0270-0255(87)90594-X
Hayat S, Imran M. On some degree based topological indices of certain nanotubes. J Comput Theor Nanosci. 2015;12(8):1599–1605. Available from: https://doi.org/10.1166/jctn.2015.3935
Hayat S, Imran M. Computation of topological indices of certain networks. Appl Math Comput. 2014;240:213–228. Available from: https://doi.org/10.1016/j.amc.2014.04.091
Liu B, Gutman I. Estimating the Zagreb and the general Randic indices. Commun Math Comput Chem. 2007;57:617–632. Available from: https://match.pmf.kg.ac.rs/electronic_versions/Match57/n3/match57n3_617-632.pdf
Matejic M, Milovanovic I, Milovanovic EI. On bounds for harmonic topological index. Filomat. 2018;32(1):311-317. Available from: http://dx.doi.org/10.2298/FIL1801311M
Vukiˇcevi´c D, Graovac A. Note on the comparison of the first and second normalized Zagreb eccentricity indices. Acta Chim Slov. 2010;57:524-528. Available from: https://acta-arhiv.chem-soc.si/57/57-3-524.pdf
Wang S, Farahani MR, Kanna MRR, Jamil MK, Kumar R.P. The Wiener index and the Hosoya polynomial of the Jahangir graphs. Appl Comput Math. 2016;5(3):138-141. Available from: https://doi.org/10.11648/j.acm.20160503.17
Xinmei L, Qian Z. The expected values for the Gutman index and Schultz index in the random regular polygonal chains. Molecules. 2022;27(20):6838. Available from: https://doi.org/10.3390/molecules27206838
Schultz HP. Topological organic chemistry 1. Graph theory and topological indices of alkanes. J Chem Inform Comput Sci. 1989;29:227-228. Available from: https://pubs.acs.org/doi/pdf/10.1021/ci00063a012
Klavˇzar S, Gutman I. Wiener number of vertex-weighted graphs and a chemical application. Disc Appl Math. 1997;80:73–81. Available from: https://doi.org/10.1016/S0166-218X(97)00070-X
Asir T, Tamizh Chelvam T. On the total graph and its complement of a commutative ring. Comm Algebra. 2013;41(10):3820–3835. Available from: https://doi.org/10.1080/00927872.2012.678956
Beck I. Coloring of a commutative ring. J Algebra. 1988;116:208-226. Available from: https://doi.org/10.1016/0021-8693(88)90202-5
Anderson DF, Livingston PS. The zero-divisor graph of commutative ring. J Algebra. 1999;217:434–447.
Ahmad A, Haider A. Computing the radio labeling associated with zero divisor graph of a commutative ring. U.P.B. Sci. Bull., Series A. 2019;81(1):65–72. Available from: https://www.scientificbulletin.upb.ro/rev_docs_arhiva/reze3e_408258.pdf
Anderson DF, Axtell MC, Stickles JA Jr. The zero-divisor graphs in commutative ring. J Algebra. 2011;217(2):434–447. Available from: https://link.springer.com/chapter/10.1007/978-1-4419-6990-3_2
Anderson DF, Mulay SB. On the diameter and girth of a zero-divisor graph. J Pure Appl Algebra. 2008;210(2):543–550. Available from: https://doi.org/10.1016/j.jpaa.2006.10.007
Rayer CJ, Jeyaraj RS. Applications on topological indices of zero-divisor graph associated with commutative rings. Adv Combin Graph Theory. 2023;15(2):335. Available from: https://doi.org/10.3390/sym15020335
Backhouse R. Principles of algorithmic problem solving. Wiley; 2012.
Elahi K, Ahmad A, Hasni R. Construction algorithm for zero divisor graphs of finite commutative rings and their vertex-based eccentric topological indices. Mathematics. 2018;6(12):301. Available from: https://doi.org/10.3390/math6120301
Todeschini R, Consonni V. Handbook of Molecular Descriptors. Weinheim: Wiley VCH; 2000. Available from: https://download.e-bookshelf.de/download/0000/6031/40/L-G-0000603140-0002364944.pdf
Cormen TH, Leiserson CE, Rivest RL, Stein C. Introduction to algorithms. 3rd ed. Cambridge (MA): The MIT Press; 2009. Available from: https://cdn.manesht.ir/19908___Introduction%20to%20Algorithms.pdf
Elahi K, Ahmad A, Asim MA, Hasni R. Computation of edge-based topological indices for zero divisor graphs of commutative rings. Ital J Pure Appl Math. 2022;48:523-534. Available from: https://ijpam.uniud.it/online_issue/202248/40%20Elahi-Ahmad-Asim-Hasni.pdf