On conditional fault tolerance and diagnosability of hierarchical cubic networks.

Fault tolerance is especially important for interconnection networks, since the growing size of networks increases their vulnerability to component failures. A classical measure for the fault tolerance of a network in the case of vertex failures is its connectivity. Given a network based on a graph G and a positive integer h, the Rh-connectivity of G is the minimum cardinality of a set of vertices in G, if any, whose deletion disconnects G, and the minimum degree of every connected component is at least h. This paper investigates the Rh-connectivity (h=1,2) of the hierarchical cubic network HCNn (n≥2), and shows that κ1(HCNn)=2n, κ2(HCNn)=4n−4, respectively. Furthermore, the paper establishes the conditional diagnosability of HCNn under the PMC diagnostic model.