Geodesic
The maximal exceptional graphs with maximal degree less than 28
Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 26 (2001) no. 1.

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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. 
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D. Cvetković; P. Rowlinson; S.K. Simić. The maximal exceptional graphs with maximal degree less than 28. Bulletin de l'Académie serbe des sciences. Classe des sciences mathématiques et naturelles, Tome 26 (2001) no. 1. http://geodesic.mathdoc.fr/item/BASS_2001_26_1_a6/