@article {
author = {Pirzada, Shariefuddin and Altaf, Aaqib and Khan, Saleem},
title = {STRUCTURE OF ZERO-DIVISOR GRAPHS ASSOCIATED TO RING OF INTEGER MODULO n},
journal = {Journal of Algebraic Systems},
volume = {11},
number = {1},
pages = {1-14},
year = {2023},
publisher = {Shahrood University of Technology},
issn = {2345-5128},
eissn = {2345-511X},
doi = {10.22044/jas.2022.11719.1599},
abstract = {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 $2<p<q<r$ are primes and $N_1$ and $N_2$ are positive integers.},
keywords = {zero-divisor graph,integers modulo ring,Eulers's totient function},
url = {https://jas.shahroodut.ac.ir/article_2662.html},
eprint = {https://jas.shahroodut.ac.ir/article_2662_5c12fb2660f3006615d619d7ebbbd933.pdf}
}