signless laplacian eigenvalues of the zero divisor graph associated to finite commutative ring zpm1 qm2

For a commutative ring r with identity 1 6= 0, let the set z(r) denote the set of zero-divisors and let z∗(r) = z(r) {0} be the set of non-zero zero divisors of r. the zero divisor graph of r, denoted by γ(r), is a simple graph whose vertex set is z∗(r) and two vertices u, v ∈ z∗(r) are adjacent if and only if uv = vu = 0. in this article, we find the signless laplacian spectrum of the zero divisor graphs γ(zn) for n = pm1 qm2 , where p < q are primes and m1, m2 are positive integers.