Abstract
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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© 1991 Springer-Verlag Berlin Heidelberg
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Baumslag, M. (1991). On the fault-tolerance of quasi-minimal cayley networks. In: Dehne, F., Fiala, F., Koczkodaj, W.W. (eds) Advances in Computing and Information — ICCI '91. ICCI 1991. Lecture Notes in Computer Science, vol 497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54029-6_192
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DOI: https://doi.org/10.1007/3-540-54029-6_192
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