Regular divisor graph of finite commutative ring
Article Sidebar
Main Article Content
Abstract
Let R be a finite commutative ring with identity 1. We introduce a new graph called regular divisor graph and denoted by . We classify the finite commutative ring to get a special graph and we are going to study some properties of this graph, clique number, chromatic number, number of cycles, connectivity and blocks.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
Tikrit Journal of Pure Science is licensed under the Creative Commons Attribution 4.0 International License, which allows users to copy, create extracts, abstracts, and new works from the article, alter and revise the article, and make commercial use of the article (including reuse and/or resale of the article by commercial entities), provided the user gives appropriate credit (with a link to the formal publication through the relevant DOI), provides a link to the license, indicates if changes were made, and the licensor is not represented as endorsing the use made of the work. The authors hold the copyright for their published work on the Tikrit J. Pure Sci. website, while Tikrit J. Pure Sci. is responsible for appreciate citation of their work, which is released under CC-BY-4.0, enabling the unrestricted use, distribution, and reproduction of an article in any medium, provided that the original work is properly cited.
References
[1] A Wardayani, I. K. I. S., 2020. Regular rings and their properties. Journal of Physics, pp. 1742-6596.
[2] Ali Jafari Taloukolaei, s. s., 2018. Von Neumann regular graphs associated with rings. Discreate Mathematics, Algorithms and Applications, 10(3).
[3] Bela Bollobas, T. C. E. B. F. G. K. R., 1998. Modern Graph Theory. s.l.:Springer Science+ Business Media.
[4] Diestel, R., 2017. Graph Theory. fifth ed. s.l.:y Springer Nature .
[5] Fournier, J.-C., 2006. Graph Theory and Applications. s.l.:Lavoisier entitled .
[6] FRANK AYRES, L. R. J., n.d. Theory and Problems of ABSTRACT ALGEBRA. 2nd ed. 2004: McGraw-Hill Companies.
[7] Haxhimusa, Y., 2006. Basics of Graph Theory. In: The Structurally Optimal Dual Graph Pyramid and its Application in Image Partitioning.. vienna: Pattern Recognition and Image Processing Group.
[8] Ian Wsye, F. t. C., 2020. On the Connectivity of Connected Bipartite Graphs With Two Orbits. *Portland State University.
[9] Marlow Anderson, T. F., 2015. A First Course in Abstract Algebra. s.l.:Taylor & Francis Group.
[10] OSAMA ALKAM, E. A. O., 2008. On the regular elements in Z_n. Turkish Journal of Mathematics, Volume 32, pp. 31-39.
[11] Reza Akhtar, L. L., 2016. Connectivity of the zero-divisor graph for finite rings. Involve, Volume 9.