On fat Hoffman graphs with smallest eigenvalue at least -3
Combinatorics
2012-10-02 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1110.6821,
title = {On fat Hoffman graphs with smallest eigenvalue at least -3},
author = {Hye Jin Jang and Jack Koolen and Akihiro Munemasa and Tetsuji Taniguchi},
journal= {arXiv preprint arXiv:1110.6821},
year = {2012}
}
Comments
23 pages, minor revision. Example 3.8 added