Some results on the non-zero divisor graphs of Zn
*Fatema A. SadiqCorresponding authorfatema.a.sadiq@uotechnology.edu.iqDepartment of Mathematics and Computer Applications College of Applied Sciences University of Technology Baghdad, IraqView full profile → , Haider A. Ramadhanhydrb5266@gmail.comDepartment of Mathematics Wasit Center Open Educational CollegeWasit, IraqView full profile → , Ali A. Aubadali.abd@sc.uobaghdad.edu.iqDepartment of Mathematics College of Science University of Baghdad Department of Mathematics College of Science University of BaghdadBaghdad, IraqView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 04 Feb 2025
- Published Online:
- 26 Jun 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-2268
- Pages:
- 1301–1307
Abstract
Keywords
Subject Classifications
References
[1] H. R. Dorbidi, “On a conjecture about the commuting graphs of finite matrix rings,” Finite Fields and Their Applications, vol. 56, pp. 93–96 (2019).
[2] A. Oudah and A. Aubad, “Analysing the structure of A4-graphs for Mathieu groups,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 24, no. 6, pp. 1907–1913 (2021).
[3] D. Azeez and A. Aubad, “Investigation of commuting graphs for elements of order 3 in certain Leech lattice groups,” Iraqi Journal of Science, vol. 62, no. 8, pp. 2640–2652 (2021).
[4] S. Kadem, A. Aubad, and A. H. Majeed, “The non-zero divisor graph of a ring,” Italian Journal of Pure and Applied Mathematics, vol. 43, pp. 975–983 (2020). [Online]. Available: https://ijpam.uniud.it/online,issue/IJPAM_no-43-.pdf#page=990.
[5] D. F. Anderson and P. S. Livingston, “The zero-divisor graph of a commutative ring,” Journal of Algebra, vol. 217, pp. 434–447 (1999). MR1700509, Zbl 0941.05062.
[6] I. Beck, “Coloring of commutative rings,” Journal of Algebra, vol. 116, no. 1, pp. 208–226 (1988). [Online]. Available: https://doi.org/10.1016/0021-8693(88)90202-5
[7] N. A. F. O. Zai, N. H. Sarmin, S. M. S. Khasraw, I. Gambo, and N. Zaid, “The non-zero divisor graph of ring of integers modulo six and the Hamiltonian quaternion over integers modulo two,” Journal of Physics: Conference Series, vol. 1988, no. 1, p. 012074 (2021). [Online]. Available: https://doi.org/10.1088/1742-6596/1988/1/012074
[8] J. Gross, J. Yellen, and M. Anderson, Graph Theory and Its Applications, 3rd ed. Boca Raton, FL, USA: Taylor & Francis, 2019.
[9] D. J. Watts and S. H. Strogatz, “Collective dynamics of ‘small-world’ networks,” Nature, vol. 393, pp. 440–442 (1998).
[10] B. K. Boruah, “Special identity subgraph in genetic code,” Network Biology, vol. 12, no. 2, pp. 45–52 (2022).
[11] B. L. Mayer and L. H. A. Monteiro, “On the divisors of natural and happy numbers: a study based on entropy and graphs,” AIMS Mathematics, vol. 8, no. 6, pp. 13411–13424 (2023).
[12] J. P. Mueller and J. Sizemore, MATLAB For Dummies. Hoboken, NJ, USA: John Wiley & Sons (2021).
[13] The MathWorks Inc., Optimization Toolbox, Version 9.4 (R2022b), Natick, MA, USA: The MathWorks Inc. (2022). [Online]. Available: https://www.mathworks.com
