Fat Hoffman graphs with smallest eigenvalue at least −1 − τ

Authors

  • Akihiro Munemasa Tohoku University, Japan
  • Yoshio Sano University of Tsukuba, Japan
  • Tetsuji Taniguchi Matsue College of Technology, Japan

DOI:

https://doi.org/10.26493/1855-3974.287.137

Keywords:

Hoffman graph, line graph, graph eigenvalue, special graph

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 − τ is an H-line graph, where H 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.

Published

2013-04-22

Issue

Section

Special Issue Bled'11