Laplacian spectrum of the unit graph associated to the ring of integers modulo $pq$

Let $R$ be a ring and $U(R)$ be the set of unit elements of $R$. The unit graph $G(R)$ of $R$ is the graph whose vertices are all the elements of $R$, defining distinct vertices $x$ and $y$ to be adjacent if and only if $x+y\in U(R)$. The Laplacian spectrum of $G({\mathbb{Z}}_n)$ was studied when $n=p^m$, where $p$ is a prime and $m$ is a positive integer. Consequently, in this paper, we study the Laplacian spectrum of $G({\mathbb{Z}}_n)$, for $n=p_1{p}_2...p_k$, where $p_i$ are distinct primes and $i=1,2,...,k$.