Embedding Cycles and Paths in a k-Ary n-Cube

摘要

The k-ary n-cube, denoted by (Q{sub}n){sup}k, has been one of the most common interconnection networks. In this paper, we study some topological properties of (Q{sub}n){sup}k. Given two arbitrary distinct nodes x and y in (Q{sub}n){sup}k, we show that there exists an x-y path of every length from [k/2]n to k{sup}n - 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 (Q{sub}n){sup}k lies on a cycle of every length from k to k{sup}n. In addition, we show that (Q{sub}n){sup}k is both bipanconnected and edge-bipancyclic, where n ≥ 2 is an integer and k ≥ 2 is an even integer.