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

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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 {\em 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

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Electronic fulltext finalized on: 20 Aug 2001. This page was last modified: 24 May 2002.

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