Split Nonthreshold Laplacian Integral Graphs
Kirkland, Stephen and de Freitas, Maria Aguieiras Alvarez and Del Vecchio, Renata Raposo and de Abreu, Nair Maria Maia (2010) Split Nonthreshold Laplacian Integral Graphs. Linear and Multilinear Algebra, 58 (2). pp. 221-233. ISSN 0308-1087
The aim of this article is to answer a question posed by Merris in European Journal of Combinatorics, 24(2003)413¡430, about the pos sibility of finding split nonthreshold 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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