It is shown, by exhibiting the list, that there are exactly 31 nonisomorphic minimal forbidden subgraphs for generalized line graphs, that is, graphs which are representable by a subset of the root system D for some n. This solves a problem n of Hoffman.Further, it is proved that the family of minimal forbidden subgraphs for graphs whose adjacency matrix has the least eigen-value at least -2, is finite.
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