On fat Hoffman graphs with smallest eigenvalue at least -3

Hye Jin Jang, Jack Koolen, Akihiro Munemasa, Tetsuji Taniguchi

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

We investigate fat Hoffman graphs with smallest eigenvalue at least -3, using their special graphs. We show that the special graph S(H) of an indecomposable fat Hoffman graph H is represented by the standard lattice or an irreducible root lattice. Moreover, we show that if the special graph admits an integral representation, that is, the lattice spanned by it is not an exceptional root lattice, then the special graph S-(H) is isomorphic to one of the Dynkin graphs An, Dn, or extended Dynkin graphs Ãn or D̃n.

Original languageEnglish
Pages (from-to)105-121
Number of pages17
JournalArs Mathematica Contemporanea
Volume7
Issue number1
Publication statusPublished - 2014 Jan 17

Keywords

  • Graph eigenvalue
  • Hoffman graph
  • Line graph
  • Root system
  • Special graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Algebra and Number Theory
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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