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. Ser. 81(95) (2007), 11-27).