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), p. 115

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Zbl

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.
Classification : 05C50
Keywords: Graph, eigenvalue, root system 
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), p. 115 . http://geodesic.mathdoc.fr/item/BASS_2001_26_a6/
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     author = {D. Cvetkovi\'c and P. Rowlinson and S.K. Simi\'c},
     title = {The maximal exceptional graphs with maximal degree less than 28},
     journal = {Bulletin de l'Acad\'emie serbe des sciences. Classe des sciences math\'ematiques et naturelles},
     pages = {115 },
     year = {2001},
     volume = {26},
     zbl = {0997.05060},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASS_2001_26_a6/}
}
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