%0 Journal Article
%T STRUCTURE OF ZERO-DIVISOR GRAPHS ASSOCIATED TO RING OF INTEGER MODULO n
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Pirzada, Shariefuddin
%A Altaf, Aaqib
%A Khan, Saleem
%D 2023
%\ 09/01/2023
%V 11
%N 1
%P 1-14
%! STRUCTURE OF ZERO-DIVISOR GRAPHS ASSOCIATED TO RING OF INTEGER MODULO n
%K zero-divisor graph
%K integers modulo ring
%K Eulers's totient function
%R 10.22044/jas.2022.11719.1599
%X For a commutative ring $R$ with identity $1\neq 0$, let $Z^{*}(R)=Z(R)\setminus \lbrace 0\rbrace$ be the set of non-zero zero-divisors of $R$, where $Z(R)$ is the set of all zero-divisors of $R$. The zero-divisor graph of $R$, denoted by $\Gamma(R)$, is a simple graph whose vertex set is $Z^{*}(R)=Z(R)\setminus \{0\}$ and two vertices of $ Z^*(R)$ are adjacent if and only if their product is $ 0 $. In this article, we find the structure of the zero-divisor graphs $ \Gamma(\mathbb{Z}_{n}) $, for $n=p^{N_1}q^{N_2}r$, where $2