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2011

Augmented k-ary n-cubes

8 years 1 months ago
Augmented k-ary n-cubes
We define an interconnection network AQn,k which we call the augmented kary 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 ⌊k 3 ⌋+⌈k−1 3 ⌉, when n = 2; and has diameter at most k 4 (n + 1), for n ≥ 3 and k even, and at most k 4 (n + 1) + n 4 , for n ≥ 3 and k odd.
Yonghong Xiang, Iain A. Stewart
Added 14 May 2011
Updated 14 May 2011
Type Journal
Year 2011
Where ISCI
Authors Yonghong Xiang, Iain A. Stewart
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