Spectrum of the zero-divisor graph on the ring of integers modulo n

Abstract

For a commutative ring R with non-zero identity, let Z∗(R) denote the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by Γ(R), is a simple undirected graph with all non-zero zero-divisors as vertices and two distinct vertices x, y ∈ Z∗(R) are adjacent if and only if xy = 0. In this paper, the adjacency matrix and spectrum of Γ(Zpk ) are investigated. Also, the implicit computation of the spectrum of Γ(Zn) is described.