On laplacian eigenvalues of the zero-divisor graph associated to the ring of integers modulo n

Abstract

Given a commutative ring R with identity 1 ≠ 0, let the set Z(R) denote the set of zerodivisors 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 Γ(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 Γ(Zn) for n = pN1 qN2, where p < q are primes and N1, N2 are positive integers.