Kirkland, Stephen and de Freitas, Maria Aguieiras Alvarez and Del Vecchio, Renata Raposo and de Abreu, Nair Maria Maia
Split Nonthreshold Laplacian Integral Graphs.
Linear and Multilinear Algebra, 58 (2).
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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