On the eigenvalues of zero-divisor graph associated to finite commutative ring

Abstract

Let Z(R) be the set of zero-divisors of a commutative ring R with non-zero identity and be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by is a simple graph whose vertex set is and two vertices are adjacent if and only if In this paper, we investigate the adjacency matrix and the spectrum of the zero-divisor graphs for where are primes and M, N are positive integers. Moreover, we obtain the clique number, stability number and girth of

Keywords

• adjacency matrix
• zero-divisor graph
• finite commutative ring
• euler's totient function