On the fault-tolerance of quasi-minimal cayley networks

  • Marc Baumslag
Parallel Processing And Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 497)


In this paper, we study the fault-tolerance of a large class of networks, whose underlying communication topology is a quasi-minimal Cayley graph, by studying their connectivity. Many “benchmark” parallel networks are included in this class, such as hypercube networks, butterfly networks, cube-connected cycles networks, double ring networks and star networks. Our main result is a proof that all quasi-minimal Cayley graphs have connectivity equal to their degree. This theorem generalizes results of Godsil [Go] and Akers and Krishnamurthy [AK]. We employ a proof technique which differs substantially from previous ones used to study the connectivity of highly symmetric graphs and, in particular, our method constitutes a more constructive approach to the problem. Based on our results, we are also led to suggest a hierarchical method for the packaging of a parallel network that provides the network with a high degree of fault-tolerance.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Marc Baumslag
    • 1
  1. 1.Graduate CenterCity University of New YorkNew York

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