On Laplacian Eigenvalues of the Zero-Divisor Graph Associated to the Ring of Integers Modulo n

Given a commutative ring R with identity 1 not equal 0, let the set Z(R) denote the set of zero-divisors and let Z*(R)=Z(R)\{0} be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by Gamma(R), is a simple graph whose vertex set is Z*(R) and each pair of vertices in Z*(R) are adjacent when their product is 0. In this article, we find the structure and Laplacian spectrum of the zero-divisor graphs Gamma(Z(n)) for n=p(N1)q(N2), where p<q are primes and N-1,N-2 are positive integers.