Augmented k-ary n-cubes |
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Authors: | Yonghong Xiang |
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Affiliation: | Department of Computer Science, University of Durham, Science Labs, South Road, Durham DH1 3LE, UK |
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Abstract: | We define an interconnection network AQn,k which we call the augmented k-ary n-cube by extending a k-ary n-cube in a manner analogous to the existing extension of an n-dimensional hypercube to an n-dimensional augmented cube. We prove that the augmented k-ary n-cube AQn,k has a number of attractive properties (in the context of parallel computing). For example, we show that the augmented k-ary n-cube AQn,k: is a Cayley graph, and so is vertex-symmetric, but not edge-symmetric unless n = 2; has connectivity 4n − 2 and wide-diameter at most max{(n − 1)k − (n − 2), k + 7}; has diameter , when n = 2; and has diameter at most , for n ? 3 and k even, and at most , for n ? 3 and k odd. |
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Keywords: | Interconnection networks Parallel computing k-ary n-cubes Augmented cubes |
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