Abstract
In this paper, we classify finite rings with upper irredundance number less than or equal to two. We note that, for such zero-divisor graphs, the upper irredundance number coincides with the independence number.
Publisher
Sociedade Paranaense de Matematica
Reference17 articles.
1. Anderson, D. F. , On the diameter and girth of a zero divisor graph II, Houston. J. Math. 34, 361-371, (2008).
2. Anderson, D. F. , Axtell, M. and Stickles, J. , Zero-divisor graphs in commutative rings, Commutative Algebra, Noetherian and Non-Noetherian Perspectives, In: Fontana M, Kabbaj SE, Olberding B, Swanson I, editors. New York, NY, USA: Springer-Verlag, pp. 23-45, 2010. https://doi.org/10.1007/978-1-4419-6990-3_2
3. Anderson, D. F. and Badawi, A., On the zero-divisor graph of a ring, Comm. Algebra 36, 3073-3092, (2008). https://doi.org/10.1080/00927870802110888
4. Anderson, D. F. and Livingston, P. S., The zero-divisor graph of a commutative ring, J. Algebra 217 , 434-447, (1999). https://doi.org/10.1006/jabr.1998.7840
5. Arumugam, S., Irredundance saturation number of a graph, Australas. J. Combin. 46, 37-49, (2010).