Adjacency matrices of zero-divisor graphs of integers modulo<i>n</i>

Abstract

We study adjacency matrices of zero-divisor graphs of [math] for various [math] . We find their determinant and rank for all [math] , develop a method for finding nonzero eigenvalues, and use it to find all eigenvalues for the case [math] , where [math] is a prime number. We also find upper and lower bounds for the largest eigenvalue for all [math] .