Remarks on Q-integral complete multipartite graphs |
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| Authors: | Milan Pokorný Pavel Híc Dragan Stevanović |
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| Institution: | 1. Trnava University, Faculty of Education, Priemyselná 4, P.O. Box 9, 918 43 Trnava, Slovakia;2. University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, 18000 Niš, Serbia;3. University of Primorska, Institute Andrej Maruši?, Muzejski trg 2, 6000 Koper, Slovenia |
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| Abstract: | A graph is Q-integral if the spectrum of its signless Laplacian matrix consists entirely of integers. In their study of Q-integral complete multipartite graphs, Zhao et al., Q-integral complete r-partite graphs, Linear Algebra Appl. 438 (2013) 1067–1077] posed two questions on the existence of such graphs. We resolve these questions and present some further results characterizing particular classes of Q-integral complete multipartite graphs. |
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| Keywords: | Signless Laplacian spectrum Integral graphs Complete multipartite graphs Seidel spectrum |
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