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

TL;DR

This paper investigates bounds for the sum of powers of Laplacian eigenvalues and the Laplacian Estrada index of graphs, providing new theoretical insights into these spectral graph invariants.

Contribution

It introduces bounds for the sum of powers of Laplacian eigenvalues and the Laplacian Estrada index based on degree sequences, extending spectral graph theory.

Findings

Established bounds for $s_{eta}(G)$ related to degree sequences.

Derived bounds for the Laplacian Estrada index.

Connected spectral invariants with graph degree properties.

Abstract

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.