New Bounds for the Signless Laplacian Spread

TL;DR

This paper introduces new theoretical bounds for the signless Laplacian spread of graphs, enhancing understanding of spectral graph properties through invariant parameters and minmax principles.

Contribution

It provides novel lower and upper bounds for the signless Laplacian spread based on graph invariants and a minmax approach.

Findings

New bounds for the signless Laplacian spread established

Bounds depend on graph invariant parameters

Minmax principle used to derive lower bounds

Abstract

Let $G$ be a simple graph. The signless Laplacian spread of $G$ is defined as the maximum distance of pairs of its signless Laplacian eigenvalues. This paper establishes some new bounds, both lower and upper, for the signless Laplacian spread. Several of these bounds depend on invariant parameters of the graph. We also use a minmax principle to find several lower bounds for this spectral invariant.