EMIS ELibM Electronic Journals Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
Vol. CXXII, No. 26, pp. 115–131 (2001)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home


Pick a mirror


The maximal exceptional graphs with maximal degree less than $28$

D. Cvetkovic, P. Rowlinson and S.K. Simic

Departemnt of Mathematics, Faculty of Electrical Engineering, University of Belgrade, P.O. Box 35-54, 11120 Belgrade, Yugoslavia
Department of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA, Scotland
Department of Mathematics, Maritime Faculty Kotor, 85 330 Kotor, Dobrota 36, Montenegro, Yugoslavia

Abstract: A graph is said to be exceptional if it is connected, has least eigenvalue greater than or equal to $-2$, and is not a generalized line graph. Such graphs are known to be representable in the root system $E_8$. The 473 maximal exceptional graphs were found initially by computer, and the 467 with maximal degree $28$ have subsequently been characterized. Here we use constructions in $E_8$ to prove directly that there are just six maximal exceptional graphs with maximal degree less than 28.

Keywords: Graph, eigenvalue, root system

Classification (MSC2000): 05C50

Full text of the article: (for faster download, first choose a mirror)

Electronic fulltext finalized on: 20 Aug 2001. This page was last modified: 20 Jun 2011.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
© 2001–2011 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition