Abstract
In this paper, we show that all fat Hoffman graphs with smallest eigenvalue at least 1-τ, where τ is the golden ratio, can be described by a finite set of fat (-1 - τ )-irreducible Hoffman graphs. In the terminology of Woo and Neumaier, we mean that every fat Hoffman graph with smallest eigenvalue at least -1-τis an H-line graph, where N is the set of isomorphism classes of maximal fat (-1 - τ )-irreducible Hoffman graphs. It turns out that there are 37 fat (-1 - τ )-irreducible Hoffman graphs, up to isomorphism.
| Original language | English |
|---|---|
| Pages (from-to) | 247-262 |
| Number of pages | 16 |
| Journal | Ars Mathematica Contemporanea |
| Volume | 7 |
| Issue number | 1 |
| Publication status | Published - 2014 Jan 17 |
Keywords
- Graph eigenvalue
- Hoffman graph
- Line graph
- Special graph
ASJC Scopus subject areas
- Theoretical Computer Science
- Algebra and Number Theory
- Geometry and Topology
- Discrete Mathematics and Combinatorics