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Citation

Cvetkovic D, Rowlinson P & Simic SK (2001) The maximal exceptional graphs with maximal degree less than 28. Bulletin, Classe des Sciences Mathematiques et Naturelles, Sciences Mathematiques, CXXII (26), pp. 115-131. http://www.emis.ams.org/journals/BSANU/26/7.html

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 E8. 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 E8 to prove directly that there are just six maximal exceptional graphs with maximal degree less than 28.

Keywords
graph; eigenvalue; root system

Journal
Bulletin, Classe des Sciences Mathematiques et Naturelles, Sciences Mathematiques: Volume CXXII, Issue 26