Note on the Sum of Powers of Signless Laplacian Eigenvalues of Graphs

TL;DR

This paper investigates bounds on the sum of powers of signless Laplacian eigenvalues of graphs, providing new theoretical insights and implications for incidence energy.

Contribution

It introduces novel bounds on the graph invariant involving signless Laplacian eigenvalues and explores their implications for incidence energy.

Findings

New bounds on $s_{\alpha}(G)$ for various graphs

Results relating $s_{\alpha}(G)$ to incidence energy

Theoretical insights into spectral graph invariants

Abstract

For a simple graph $G$ and a real number $\alpha $ $\left(\alpha \neq 0,1\right) $ the graph invariant $s_{\alpha}\left(G\right) $ is equal to the sum of powers of signless Laplacian eigenvalues of $G$. In this note, we present some new bounds on $s_{\alpha}\left(G\right) $. As a result of these bounds, we also give some results on incidence energy.