CYCLE AND PATH EMBEDDING ON 5-ARY N-CUBES

摘要

We study two topological properties of the 5-ary n-cube Q_n~5. Given two arbitrary distinct nodes x and y in Q_n~5, we prove that there exists an x-y path of every length ranging from 2n to 5~n -1, where n ≥ 2. Based on this result, we prove that Q_n~5 is 5-edge-pancyclic by showing that every edge in Q_n~5 lies on a cycle of every length ranging from 5 to 5~n.