  We study the Laplacian eigenvalues of the zero divisor graph
$\Gamma\left(\mathbb{Z}_{n}\right)$ of the ring $\mathbb{Z}_{n}$ and prove that
$\Gamma\left(\mathbb{Z}_{p^t}\right)$ is Laplacian integral for every prime $p$
and positive integer $t\geq 2$. We also prove that the Laplacian spectral
radius and the algebraic connectivity of $\Gamma\left(\mathbb{Z}_{n}\right)$
for most of the values of $n$ are, respectively, the largest and the second
smallest eigenvalues of the vertex weighted Laplacian matrix of a graph which
is defined on the set of proper divisors of $n$. The values of $n$ for which
algebraic connectivity and vertex connectivity of
$\Gamma\left(\mathbb{Z}_{n}\right)$ coincide are also characterized.
