We study two topological properties of the 5-ary n-cube Qn 5. Given two arbitrary distinct nodes x and y in Qn 5, we prove that there exists an x-y path of every length ranging from 2n to 5n-1, where n≥2. Based on this result, we prove that Qn5 is 5-edge-pancyclic by showing that every edge in Qn5 lies on a cycle of every length ranging from 5 to 5n.
All Science Journal Classification (ASJC) codes
- Computer Science Applications