Panconnectivity and edge-pancyclicity of 3-ary N-cubes
We study two topological properties of the 3-ary n-cube Q(n)(3). Given two arbitrary distinct nodes x and y in Q(n)(3), we prove that there exists an x-y path of every length ranging from d( x, y) to 3(n)-1, where d( x, y) is the length of a shortest path between x and y. Based on this result, we prove that Q(n)(3) is edge-pancyclic by showing that every edge in Q(n)(3) n lies on a cycle of every length ranging from 3 to 3(n).
panconnectivity edge-pancyclicity graph-theoretic interconnection networks hypercubes k-ary n-cubes