The Bounds for Eigenvalues of Normalized and Signless Laplacian Matrices

TL;DR

This paper derives bounds for the extreme and k-th eigenvalues of normalized and signless Laplacian matrices using trace-based methods, advancing spectral graph theory understanding.

Contribution

It introduces new bounds for eigenvalues of normalized and signless Laplacian matrices, including for the k-th eigenvalues, using trace techniques.

Findings

Bounds for the largest and smallest eigenvalues are established.

Bounds for the k-th eigenvalues are determined.

Trace methods effectively estimate spectral extremities.

Abstract

In this paper, we obtain the bounds of the extreme eigenvalues of a normalized and signless Laplacian matrices using by their traces. In addition, we determine the bounds for k-th eigenvalues of normalized and signless Laplacian matrices.