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.