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. [R Hansen, H. Melot, D. Stevanovic, 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 K-n1, boolean OR (K-n2 boolean OR K-n3), where K-ni, i = 1, 2, 3, is a complete graph on n(i) vertices. These characterizations allow us to exhibit many infinite families of Q-integral graphs. (C) 2009 Elsevier Inc. All rights reserved.