Large butterfly Cayley graphs and digraphs

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We present families of large undirected and directed Cayley graphs whose construction is related to butterfly networks. One approach yields, for every large k and for values of d taken from a large interval, the largest known Cayley graphs and digraphs of diameter k and degree d. Another method yields, for sufficiently large k and infinitely many values of d, Cayley graphs and digraphs of diameter k and degree d whose order is exponentially larger in k than any previously constructed. In the directed case, these are within a linear factor in k of the Moore bound.
Original languageEnglish
Pages (from-to)2432-2436
Number of pages5
JournalDiscrete Mathematics
Issue number10
Early online date24 Jun 2017
Publication statusPublished - 1 Oct 2017


  • Cayley graphs
  • degree–diameter problem
  • butterfly networks
  • Moore bound


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