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Keywords:

  • simple graph;
  • hypercube;
  • distance;
  • diameter;
  • connectivity;
  • routing;
  • broadcasting;
  • embedding

Abstract

Following the recursive definition of the hypercube Qn, we define the augmented cube AQn. After showing that its graph is vertex-symmetric, (2n − 1)-regular, and (2n − 1)-connected and that it has diameter ⌈n/2⌉, we describe optimal routing and broadcasting procedures. The augmented cube possesses several embeddable properties that the hypercube and its variations do not possess. © 2002 Wiley Periodicals, Inc.