Abstract
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 K n 1 ∨ ( K n 2 ∪ K n 3 ) , where K n i , 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.
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