Critical groups of generalized de Bruijn and Kautz graphs and circulant matrices over finite fields

  • Swee Hong Chan
  • Henk D. L. Hollmann
  • Dmitrii V. Pasechnik
Part of the CRM Series book series (PSNS, volume 16)


We determine the critical groups of the generalized de Bruijn graphs DB(n, d) and generalized Kautz graphs Kautz (n, d), thus extending and completing earlier results for the classical de Bruijn and Kautz graphs. Moreover, for a prime p the critical groups of DB(n, p) are shown to be in close correspondence with groups of n × n circulant matrices over Fp, which explains numerical data in [11] and suggests the possibility to construct normal bases in Fp n from spanning trees in DB(n, p).


Normal Basis Critical Group Circulant Matrix Integral Matrix Circulant Matrice 
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Copyright information

© Scuola Normale Superiore Pisa 2013

Authors and Affiliations

  • Swee Hong Chan
    • 1
  • Henk D. L. Hollmann
    • 1
  • Dmitrii V. Pasechnik
    • 1
  1. 1.School of Physical and Mathematical SciencesNanyang Technological UniversitySingapore

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