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 exceptional root system E 8. We determine the maximal exceptional graphs by a computer search using the star complement technique, and then show how they can be found by theoretical considerations using a representation of E 8 in R 8. There are exactly 473 maximal exceptional graphs.
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