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A combinatorial study of substar reliability of the star network

Hierarchical networks may be divided into subnetworks having the same topological properties of the original network. The star graph, an example of hierarchical networks, has been studied extensively as a viable candidate for massively parallel systems. For a given number of faulty links and using a combinatorial approach, lower bounds on probability of having one or more (n − 1)-stars in an n-star are determined. An identification algorithm is presented to find an available (n − 1)-star in an n-star containing a set of faulty links.