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

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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)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.

Keywords:	Split graph; threshold graph; semiregular graph; Laplacian integral graph; block design;
Subjects:	Science & Engineering > Hamilton Institute
ID Code:	2190
Deposited By:	Professor Steve Kirkland
Deposited On:	13 Oct 2010 16:45
Journal or Publication Title:	Linear and Multilinear Algebra
Publisher:	Taylor & Francis
Refereed:	No
URL:	http://www.informaworld.com/smpp/title~content=t713644116~db=all

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Split Nonthreshold Laplacian Integral Graphs

Abstract