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The fault-tolerant bipancyclicity of the even kary ncube

The interconnection network considered in this paper is the k-ary n-cube that is an attractive variance of the well-known hypercube. Many interconnection networks, including the ring, the torus and the hypercube, that are attractive in both theoretical interests and practical systems can be regarded as the subclasses of the k-ary n-cubes. In this paper, we investigate the fault tolerant cycle embedding properties of the k-ary n-cubes. We show that the k-ary n-cube is (2n-2)-edge-fault bipancyclic for k is even and n 3 2. That is, it embeds all cycles of even lengths ranging from 4 to N, where N is the order of the network when there exists at most 2n-2 edge faults. Since the degree of the k-ary n-cube is 2n, the result is optimal.