Embedding cycles and paths in a k-ary n-cube

The k-ary n-cube, denoted by Q_n ^k, has been one of the most common interconnection networks. In this paper, we study some topological properties of Q_n ^k. Given two arbitrary distinct nodes x and y in Q_n ^k, we show that there exists an x-y path of every length from [k/2]n to kⁿ - 1, where n ges 2 is an integer and k ges 3 is an odd integer. Based on this result, we further show that each edge in Q_n ^k lies on a cycle of every length from k to kⁿ. In addition, we show that Q_n ^k is both bipanconnected and edge-bipancyclic, where n ges 2 is an integer and k ges 2 is an even integer.