On three conjectures involving the signless Laplacian spectral radius of graphs

We study the signless Laplacian spectral radius of graphs and prove three conjectures of Cvetkovic, Rowlinson, and Simic [Eigenvalue bounds for the signless Laplacian, Publ. Inst. Math., Nouv. S?r. 81(95) (2007), 11-27].