Embedding cycles and paths in a k-ary n-cube
Sun‐Yuan Hsieh, Tsong‐Jie Lin · 2007
The k-ary n-cube, denoted by Qnk, has been one of the most common interconnection networks. In this paper, we study some topological properties of Qnk. Given two arbitrary distinct nodes x and y in Qnk, we show that there exists an x–y path of every length from [k/2]n to kn− 1, where n ≥ 2 is an integer and k ≥ 3 is an odd integer. Based on this result, we further show that each edge in Qnklies on a cycle of every length from k to kn. In addition, we show that Qnkis both bipanconnected and edge-bipancyclic, where n ≥ 2 is an integer and k ≥ 2 is an even integer.