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Durham University

Computer Science


Publication details for Professor Iain Stewart

Xiang, Y. & Stewart, I.A. (2011). Augmented k-ary n-cubes. Information Sciences 181(1): 239-256.

Author(s) from Durham


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); has connectivity 4n-2, and is such that we can build a set of 4n-2 mutually disjoint paths joining any two distinct vertices so that the path of maximal length has length 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(n+1)/4, for n ≥ 3 and k even, and at most k(n+1)/4+n/4, for n ≥ 3 and k odd.


Available online 8 September 2010.