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

The maximal exceptional graphs with maximal degree less than $28$D. Cvetkovic, P. Rowlinson and S.K. SimicDepartemnt of Mathematics, Faculty of Electrical Engineering, University of Belgrade, P.O. Box 3554, 11120 Belgrade, YugoslaviaDepartment 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
