On fat Hoffman graphs with smallest eigenvalue at least -3

Authors

  • Hye Jin Jang POSTECH, South Korea
  • Jack Koolen POSTECH, South Korea
  • Akihiro Munemasa Tohoku University, Japan
  • Tetsuji Taniguchi Matsue College of Technology, Japan

DOI:

https://doi.org/10.26493/1855-3974.262.a9d

Keywords:

Hoffman graph, line graph, graph eigenvalue, special graph, root system

Abstract

We investigate fat Hoffman graphs with smallest eigenvalue at least −3, using their special graphs. We show that the special graph S(Ho) of an indecomposable fat Hoffman graph Ho 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 − (Ho) is isomorphic to one of the Dynkin graphs An, Dn, or extended Dynkin graphs Ãn or D̃n.

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Published

2012-12-25

Issue

Vol. 7 No. 1 (2014)

Section

Special Issue Bled'11

License

Articles in this journal are published under Creative Commons Attribution 4.0 International License
https://creativecommons.org/licenses/by/4.0/