Affiliation:
1. Department of Mathematics , University of Kashmir , Srinagar , Kashmir , India
Abstract
Abstract
For a commutative ring R with identity 1, the zero-divisor graph of R, denoted by Γ(R), is a simple graph whose vertex set is the set of non-zero zero divisors Z*(R) and the two vertices x and y ∈ Z*(R) are adjacent if and only if xy = 0. In this paper, we compute the values of some graph parameters of the zero-divisor graph associated to the ring of Gaussian integers modulo n, ℤn[i] and the ring of integers modulo n, ℤn.
Reference11 articles.
1. [1] D. F. Anderson, P. S. Livingston. The zero-divisor graph of a commutative ring, J. Algebra 217 (1999) 434–447. ⇒7510.1006/jabr.1998.7840
2. [2] M. I, Bhat, S. Pirzada, A. M. Alghamdi. On planarity of compressed zero-divisor graphs associated to commutative rings, Creative Math. Infor. 29, 2 (2020) 131–136. ⇒7810.37193/CMI.2020.02.03
3. [3] H. J. Chiang-Hsieh, H-J. Wang, Commutative rings with toroidal zero-divisor graphs, Houst. J. Math. 36, 1 (2010) 1–31. ⇒78
4. [4] J. Cross, The Euler ϕ-function in the Gaussian integers, Amer. Math. Monthly 90, 8 (1983) 518–528. ⇒7710.1080/00029890.1983.11971275
5. [5] A. Duane, Proper colorings and p-partite structures of the zero-divisor graph, Rose-Hulman Undergraduate Mathematics Journal 7, 2 (2006) Art. 16. ⇒76