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.
|ジャーナル||Ars Mathematica Contemporanea|
|出版ステータス||Published - 2014 1 17|
ASJC Scopus subject areas
- Theoretical Computer Science
- Algebra and Number Theory
- Geometry and Topology
- Discrete Mathematics and Combinatorics