On sum of powers of Laplacian eigenvalues and Laplacian Estrada index of graphs

Abstract

Let $G$ be a simple graph and $α$ a real number. The quantity $s_α(G)$ defined as the sum of the $α$-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 $s_α$ and Laplacian Estrada index related to the degree sequences.

9 pages