Hye Jin Jang, Jack Koolen, Akihiro Munemasa, Tetsuji Taniguchi
Published 2011-10-31, updated 2012-09-28Version 3
We investigate fat Hoffman graphs with smallest eigenvalue at least -3, using their special graphs. We show that the special graph S(H) of an indecomposable fat Hoffman graph H is represented by the standard lattice or an irreducible root lattice. Moreover, we show that if the special graph admits an integral representation, that is, the lattice spanned by it is not an exceptional root lattice, then the special graph S(H) is isomorphic to one of the Dynkin graphs A_n, D_n, or extended Dynkin graphs A_n or D_n.
Comments: 23 pages, minor revision. Example 3.8 added
Sesqui-regular graphs with smallest eigenvalue at least $-3$
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Max k-cut and the smallest eigenvalue
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