Path and Cycle Embedding of 3-ary N-cubes
Sun‐Yuan Hsieh, Tsong‐Jie Lin · 2007
We study two topological properties of the 3-ary n-cube Qn3. Given two arbitrary distinct nodes x and y in Qn3, we prove that there exists an x-y path of every length ranging from n to 3n- 1. Based on this result, we prove that Qn3is edge-pancyclic by showing that every edge in Qn3lies on a cycle of every length ranging from 3 to 3n.