Split non-threshold Laplacian integral graphs |
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| Authors: | Stephen Kirkland Maria Aguieiras Alvarez de Freitas Renata Raposo Del Vecchio |
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| Institution: | 1. Department of Mathematics and Statistics , University of Regina , Regina, Canada;2. Production Engineering Programme, Federal University of Rio de Janeiro , Rio de Janeiro, Brazil;3. Mathematics Institute, Fluminense Federal University , Niterói, Brazil |
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| Abstract: | The aim of this article is to answer a question posed by Merris in European Journal of Combinatorics, 24 (2003) pp. 413 ? 430, about the possibility of finding split non-threshold graphs that are Laplacian integral, i.e. graphs for which the eigenvalues of the corresponding Laplacian matrix are integers. Using Kronecker products, balanced incomplete block designs, and solutions to certain Diophantine equations, we show how to build infinite families of these graphs. |
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| Keywords: | split graph threshold graph semiregular graph Laplacian integral graph block design |
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