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Kirkland, Stephen, de Freitas, Maria Aguieiras Alvarez , 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 |
| Related URLs: | |
| URI: | https://mu.eprints-hosting.org/id/eprint/2190 |
| 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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