On the Aα spectrum of the zero-divisor graphs

Abstract

Let [Formula: see text] be a commutative ring with nonzero identity and [Formula: see text] be the set of all nonzero zero-divisors of [Formula: see text]. The zero-divisor graph of [Formula: see text], denoted by [Formula: see text], is a simple graph whose vertex set consists of all elements of [Formula: see text], and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text]. In this paper, we investigate the [Formula: see text]-spectral of the zero-divisor graph of the ring [Formula: see text]. Specially, we study the [Formula: see text]-spectral of the zero-divisor graph of the ring [Formula: see text] for [Formula: see text], [Formula: see text], [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are distinct prime numbers and [Formula: see text]. Moreover, we study the [Formula: see text]-spectral of the zero-divisor graph of the ring [Formula: see text], where [Formula: see text] is a prime number and [Formula: see text].