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Algorithm for Visualization of Zero Divisor Graphs of the Ring ℤn Using MAPLE Coding

DOI: 10.4236/ojdm.2024.141001, PP. 1-8

Keywords: Zero Divisor Graph, Ring Theory, Maple Algorithm,n Modulo n, Graph Theory, Mathematical Computing

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Abstract:

This research investigates the comparative efficacy of generating zero divisor graphs (ZDGs) of the ring of integers ?n modulo n using MAPLE algorithm. Zero divisor graphs, pivotal in the study of ring theory, depict relationships between elements of a ring that multiply to zero. The paper explores the development and implementation of algorithms in MAPLE for constructing these ZDGs. The comparative study aims to discern the strengths, limitations, and computational efficiency of different MAPLE algorithms for creating zero divisor graphs offering insights for mathematicians, researchers, and computational enthusiasts involved in ring theory and mathematical computations.

References

[1]  Ali, N., Siddiqui, H.M.A. and Qureshi, M.I. (2023) A Graph-Theoretic Approach to Ring Analysis: Dominant Metric Dimensions in Zero-Divisor Graphs. arXiv: 2312.16005.
[2]  Ali, N., Kousar, Z., Safdar, M., Tolasa, F.T. and Suleiman, E. (2023) Mapping Connectivity Patterns: Degree-Based Topological Indices of Corona Product Graphs. Journal of Applied Mathematics, 2023, Article ID: 8975497.
https://doi.org/10.1155/2023/8975497
[3]  Anderson, D.F. and Livingston, P.S. (1999) The Zero Divisor Graph of a Commutative Ring. Journal of Algebra, 217, 434-447.
https://doi.org/10.1006/jabr.1998.7840
[4]  Anderson, D.F. and LaGrange, J.D. (2012) Commutative Boolean Monoids, Reduced Rings and the Compressed Zero-Divisor Graphs. Journal of Pure and Applied Algebra, 216, 1626-1636.
https://doi.org/10.1016/j.jpaa.2011.12.002
[5]  Anderson, D.F. and LaGrange, J.D. (2016) Some Remarks on the Compressed Zero-Divisor Graphs. Journal of Algebra, 447, 297-321.
https://doi.org/10.1016/j.jalgebra.2015.08.021
[6]  Anderson, D.D. and Naseer, M. (1993) Beck’s Coloring of a Commutative Ring. Journal of Algebra, 159, 500-514.
https://doi.org/10.1006/jabr.1993.1171
[7]  Atiyah, M.F. and MacDonald, I.G. (1969) Introduction to Commutative Algebra. Addison-Wesley, Boston.
[8]  Beck, I. (1988) Coloring of Commutative Rings. Journal of Algebra, 26, 208-226.
https://doi.org/10.1016/0021-8693(88)90202-5
[9]  Chartrand, G., Eroh, L., Johnson, M.A. and Oellermann, O.R. (2000) Resolvability in Graphs and Metric Dimension of a Graph. Discrete Applied Mathematics, 105, 99-113.
https://doi.org/10.1016/S0166-218X(00)00198-0
[10]  Krone, J. (2015) Algorithms for Constructing Zero-Divisor Graphs of Commutative Rings.
http://personal.denison.edu/~krone/docs/Zero-Divisor.pdf
[11]  Kelenc, A., Tratnik, N. and Yero, I.G. (2018) Uniquely Identifying the Edges of a Graph: The Edge Metric Dimension. Discrete Applied Mathematics, 251, 204-220.
https://doi.org/10.1016/j.dam.2018.05.052
[12]  Saeed, R., Riaz, A., Lodhi, R.N., Munir, H.M. and Iqbal, A. (2014) Determinants of Dividend Payouts in Financial Sector of Pakistan. Journal of Basic and Applied Scientific Research, 4, 33-42.
[13]  Mahboob, A., Hussain, T., Akram, M., Mahboob, S., Ali, N. and Raza, A. (2020) Characterizations of Chevalley Groups Using Order of the Finite Groups. Journal of Prime Research in Mathematics, 16, 46-51.
[14]  Maimani, H.R., Pournaki, M.R. and Yassemi, S. (2006) Zero Divisor Graph with Respect to an Ideal. Communications in Algebra, 34, 923-929.
https://doi.org/10.1080/00927870500441858
[15]  Mulay, S.B. (2002) Cycles and Symmetries of Zero-Divisors. Communications in Algebra, 30, 3533-3558.
https://doi.org/10.1081/AGB-120004502
[16]  Pirzada, S. (2012) An Introduction to Graph Theory. Universities Press, Orient Blackswan, Hyderabad.
[17]  Pirzada, S., Raja, R. and Redmond, S.P. (2014) Locating Sets and Numbers of Graphs Associated to Commutative Rings. Journal of Algebra and Its Applications, 13, Article ID: 1450047.
https://doi.org/10.1142/S0219498814500479
[18]  Pirzada, S. and Raja, R. (2016) On Graphs Associated with Modules Over Commutative Rings. Journal of the Korean Mathematical Society, 53, 1167-1182.
https://doi.org/10.4134/JKMS.j150457
[19]  Pirzada, S. and Raja, R. (2017) On the Metric Dimension of a Zero Divisor Graph. Communications in Algebra, 45, 1399-1408.
https://doi.org/10.1080/00927872.2016.1175602
[20]  Pirzada, S., Raja, R. and Redmond, S. (2016) On Locating Numbers and Codes of Zero Divisor Graphs Associated with Commutative Rings. Journal of Algebra and Its Applications, 15, Article ID: 1650014.
https://doi.org/10.1142/S0219498816500146
[21]  Pirzada, S. and Raja, R. (2017) On the Metric Dimension of a Zero Divisor Graph. Communications in Algebra, 45, 1399-1408.
[22]  Redmond, S.P. (2007) On Zero-Divisor Graphs of Small Finite Commutative Rings. Discrete Mathematics, 307, 1155-1166.
https://doi.org/10.1016/j.disc.2006.07.025
[23]  Safdar, M., Mushtaq, T., Ali, N. and Akgül, A. (2023) On Study of Flow Features of Hybrid Nanofluid Subjected to Oscillatory Disk. International Journal of Modern Physics B, Article ID: 2450356.
https://doi.org/10.1142/S0217979224503569

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