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Infinite families of -integral graphs

✍ Scribed by Maria Aguieiras A. de Freitas; Nair M.M. de Abreu; Renata R. Del-Vecchio; Samuel Jurkiewicz

Publisher: Elsevier Science
Year: 2010
Tongue: English
Weight: 152 KB
Volume: 432
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2009.06.029

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✦ Synopsis

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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