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.