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 ⌊ 3 ⌋+⌈ 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. keywords: interconnection networks; parallel computing; k-ary n-cubes; augmented cubes.