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A number of existing multiprocessors are based on the hypercube interconnection network. The popularity of the hypercube is due to its small communication diameter, which grows logarithmically with the cube size, its fault-tolerant properties, and its modularity which makes it possible to build a larger cube from smaller subcubes. The star graph has been studied as a network topology for fault-tolerant parallel com puting. Unfortunately, the size of the network grows too sharply with n to be affordable for values of n larger than 7 or 8. We introduce a novel intercon nection network known as the incomplete star graph, which overcomes the above problem while retaining the most of the advantages of the star graph. We present the architecture of the incomplete star graph and compare its performance with the full star as well as competing architectures such as the incomplete hyÂ¿ percube and arrangement graphs. We provide routing algorithms for both non-faulty and faulty incompletestar graphs, and study their performance.