New Bounds for the Signless Laplacian Spread

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.