Theoretical Research on Topological Properties of Generalized K-Ary n-Cube Interconnection Network

The k-ary n-cube interconnection network has been widely used in the multi-computer and parallel processing system. When the numbers of the nodes at some dimensions in the k-ary n-cube network are different, the generalized K-ary n-cube interconnection network is proposed and defined using cross product of the cycles. Some topological properties of this new network were proved, then a recursive expression of surface area and volume in the network were proposed and proved. At last, the non-recursive expression of the surface area and volume in the k-ary n-cube network were proved.