Let $\lambda^G_1 > \lambda^G_2 > \dots$ be the eigenvalues of the Laplacian matrix $G$ of a graph on $n$ vertices.

Let $\mu(G)$ be the composition $a_1,\dots,a_k$ of $n$ where $a_i$ is the multiplicity of $\lambda^G_i$.

Is $\mu$ surjective as a map from (finite) simple graphs to integer compositions?