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 An, Dn, or extended Dynkin graphs Ãn or D̃n.
| Original language | English |
|---|---|
| Pages (from-to) | 105-121 |
| Number of pages | 17 |
| Journal | Ars Mathematica Contemporanea |
| Volume | 7 |
| Issue number | 1 |
| Publication status | Published - 2014 Jan 17 |
Keywords
- Graph eigenvalue
- Hoffman graph
- Line graph
- Root system
- Special graph
ASJC Scopus subject areas
- Theoretical Computer Science
- Algebra and Number Theory
- Geometry and Topology
- Discrete Mathematics and Combinatorics