Infinite families of Q-integral graphs

In this article, we characterize all signless Laplacian integral graphs (here called Q-integral graphs) in the following classes: complete split graphs, multiple complete split-like graphs, extended complete split-like graphs, multiple extended split-like graphs. All these graphs were defined by Hansen et al. [P. Hansen, H. Melot, D, Stevanović, Integral complete split graphs, Univ. Beograd, Publ. Elektrotehn. Fak. Ser. Mat. 13 (2002) 89-95]. Also, we characterize all Q-integral graphs of the form Kn1∨(Kn2∪Kn3), where , is a complete graph on ni vertices. These characterizations allow us to exhibit many infinite families of Q-integral graphs.