STRUCTURE OF ZERO-DIVISOR GRAPHS ASSOCIATED TO RING OF INTEGER MODULO n

For a commutative ring R with identity 1 ̸= 0, let Z∗(R) = Z(R) \ {0} 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 Γ(R), is a simple graph whose vertex set is Z∗(R) = Z(R) \ {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 Γ(Zn), for n = pN1 qN2 r, where 2 p q r are primes and N1 and N2 are positive integers.