On graphs associated to ring of Guassian integers and ring of integers modulo n

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.