Fat hoffman graphs with smallest eigenvalue at least -1 - τ

Akihiro Munemasa, Yoshio Sano, Tetsuji Taniguchi

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

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 languageEnglish
Pages (from-to)247-262
Number of pages16
JournalArs Mathematica Contemporanea
Volume7
Issue number1
Publication statusPublished - 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

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