Investigating topological spaces arising from commutative rings via associated zero divisor graphs : A holistic approach
*Nasir AliCorresponding authornasirzawar@gmail.comDepartment of MathematicsVehari CampusCOMSATS University IslamabadVehari, Punjab, 61100, Pakistan0000-0003-4116-9673View full profile → , Maysoon QousiniM.qousini@zuj.edu.joFaculty of Science and Information TechnologyAl-zaytoonah University of JordanAmman, 11183, Jordan0000-0001-6658-2654View full profile → , Muhammad Imran Qureshiimranqureshi18@gmail.comDepartment of MathematicsVehari CampusCOMSATS University IslamabadVehari, Punjab, 61100, Pakistan0000-0002-0681-6313View full profile → , Hafiz Muhammad Afzal Siddiquihmasiddiqui@gmail.comDepartment of MathematicsLahore CampusCOMSATS University IslamabadLahore, Punjab, 54000, Pakistan0000-0003-1794-6460View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 07 May 2024
- Published Online:
- 28 Apr 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2161
- Pages:
- 279–312
Abstract
Keywords
Subject Classifications
References
[1] A. De Schepper, J. Schillewaert, and H. Van Maldeghem, “On the Generating Rank and Embedding Rank of the Hexagonic Lie Incidence Geometries,” Combinatorica, pp. 1–38 (2024).
[2] H. A.-H. Mahdi and S. N. F. Al-khafaji, “Construction A Topology On Graphs,” J. Al-Qadisiyah Comput. Sci. Math., vol. 5, no. 2, pp. 39–46 (2013).
[3] K. Kruse, “Mixed topologies on saks spaces of vector-valued functions,” Topol. Appl., vol. 345, p. 108843 (2024).
[4] M. Bonatto, D. Dikranjan, and D. Toller, “Groups with cofinite Zariski topology and potential density,” Topol. Appl., vol. 340, p. 108720 (2023).
[5] D. F. Anderson and P. S. Livingston, “The zero-divisor graph of a commutative ring,” J. Algebra, vol. 217, pp. 434–447 (1999).
[6] D. Dikranjan and W. Tholen, “Categorical Structure of Closure Operators”. Dordrecht, Boston: Kluwer Academic Publishers (1995).
[7] S. A. Morris, “Topology Without Tears” (2017).
[8] J. Jokela, “Compatible topologies on mixed lattice vector spaces,” Topol. Appl., vol. 320 (2022).
[9] L. H. Rowen, “Ring Theory”. Academic Press, vol. 83 (2012).
[10] N. Ali, H. M. A. Siddiqui, and M. I. Qureshi, “A Graph-Theoretic Approach to Ring Analysis: Dominant Metric Dimensions in Zero-Divisor Graphs,” arXiv preprint, arXiv:2312.16005 (2023).
[11] I. Beck, “Coloring of commutative rings,” J. Algebra, vol. 26, pp. 208–226 (1988).
[12] D. D. Anderson and M. Naseer, “Beck’s coloring of a commutative ring,” J. Algebra, vol. 159, pp. 500–514 (1993).
[13] S. P. Redmond, “On zero divisor graph of small finite commutative rings,” Discrete Math., vol. 307, pp. 1155–1166 (2007).
[14] A. Mukhtar, R. Murtaza, S. U. Rehman, S. Usman, and A. Q. Baig, “Computing the size of zero divisor graphs,” J. Inf. Optim. Sci., vol. 41, no. 4, pp. 855–864 (2020).
[15] N. Annamalai and C. Durairajan, “Codes from the Incidence Matrices of a zero-divisor Graphs,” J. Discrete Math. Sci. Cryptogr., pp. 1–9 (2022).
[16] P. D. Khandare, S. M. Jogdand, and R. A. Muneshwar, “Energy and Wiener index of divisor graph of commutative ring.”
