NEW BOUNDS FOR THE SPREAD OF THE SIGNLESS LAPLACIAN SPECTRUM

The spread of the singless Laplacian of a simple graph G is defined as SQ(G) = mu(1)(G) - mu(n)(G), where mu(1)(G) and mu(n)(G) are the maximum and minimum eigenvalues of the signless Laplacian matrix of G, respectively. In this paper, we will present some new lower and upper bounds for SQ(G) in terms of clique and independence numbers. In the final section, as an application of the theory obtained in here, we will also show some new upper bounds for the spread of the singless Laplacian of tensor products of any two simple graphs.