Function of eigenvalues of Laplacian matrix

Question

Let $G$ be a simple $n$-vertex graph and let $\mu_n\geq\mu_{n-1}\geq\dots\geq\mu_1$ be the eigenvalues of its Laplacian matrix, how can I find a function $$f(\mu_1,\mu_2,\dots\mu_n) \text{ such that } e(G)= f(\mu_1,\mu_2,\dots\mu_n)?$$

Answer 1

Since the number of edges $e(G)$ equals the trace of Laplacian matrix of $G$ divided by 2, we have $$f(\mu_1,\mu_2,\dots\mu_n) = \frac{\mu_1+\mu_2+\cdots+\mu_n}2.$$