English

Fat Hoffman graphs with smallest eigenvalue at least $-1-\tau$

Combinatorics 2015-03-19 v4 Discrete Mathematics

Abstract

In this paper, we show that all fat Hoffman graphs with smallest eigenvalue at least -1-\tau, where \tau is the golden ratio, can be described by a finite set of fat (-1-\tau)-irreducible Hoffman graphs. In the terminology of Woo and Neumaier, we mean that every fat Hoffman graph with smallest eigenvalue at least -1-\tau is an H-line graph, where H is the set of isomorphism classes of maximal fat (-1-\tau)-irreducible Hoffman graphs. It turns out that there are 37 fat (-1-\tau)-irreducible Hoffman graphs, up to isomorphism.

Cite

@article{arxiv.1111.7284,
  title  = {Fat Hoffman graphs with smallest eigenvalue at least $-1-\tau$},
  author = {Akihiro Munemasa and Yoshio Sano and Tetsuji Taniguchi},
  journal= {arXiv preprint arXiv:1111.7284},
  year   = {2015}
}

Comments

19 pages, 10 figures

R2 v1 2026-06-21T19:44:14.788Z