TY - JOUR
ID - 2662
TI - STRUCTURE OF ZERO-DIVISOR GRAPHS ASSOCIATED TO RING OF INTEGER MODULO n
JO - Journal of Algebraic Systems
JA - JAS
LA - en
SN - 2345-5128
AU - Pirzada, Shariefuddin
AU - Altaf, Aaqib
AU - Khan, Saleem
AD - Department of Mathematics, University of Kashmir, Srinagar, India.
Y1 - 2023
PY - 2023
VL - 11
IS - 1
SP - 1
EP - 14
KW - zero-divisor graph
KW - integers modulo ring
KW - Eulers's totient function
DO - 10.22044/jas.2022.11719.1599
N2 - 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