  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.
