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.

Item Type:	Article
Keywords:	Split graph; threshold graph; semiregular graph; Laplacian integral graph; block design;
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	2190
Depositing User:	Professor Steve Kirkland
Date Deposited:	13 Oct 2010 15:45
Journal or Publication Title:	Linear and Multilinear Algebra
Publisher:	Taylor & Francis
Refereed:	No
URI:	http://www.informaworld.com/smpp/title~c...
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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