  Let $G$ be a simple graph and $\alpha$ a real number. The quantity
$s_{\alpha}(G)$ defined as the sum of the $\alpha$-th power of the non-zero
Laplacian eigenvalues of $G$ generalizes several concepts in the literature.
The Laplacian Estrada index is a newly introduced graph invariant based on
Laplacian eigenvalues. We establish bounds for $s_{\alpha}$ and Laplacian
Estrada index related to the degree sequences.
