Characteristic polynomials of some algebraic graphs

Abstract

The zero divisor graph Γ(R) of a commutative ring R is a graph whose vertices are non-zero zero divisors of R and two vertices are adjacent if their product is zero. The characteristic polynomial of matrix M is defined as |λI −M| and roots of the characteristic polynomial are known as eigenvalues of M. We investigate eigenvalues and characteristic polynomials for some zero divisor graphs.