Geodesic pancyclicity of twisted cubes
The hypercube is one of the most popular interconnection networks since it has simple structure and is easy to implement. An n-dimensional twisted cube, TQ(n,) is an important variation of the hypercube Q(n) and preserves many of its desirable properties. The problem of embedding linear arrays and cycles into a host graph has attracted substantial attention in recent years. The geodesic cycle embedding problem is for any two distinct vertices, to find all the possible lengths of cycles that include a shortest path joining them. In this paper, we prove that TQ(n) is geodesic 2-pancyclic for each odd integer n >= 3. This result implies that TQ(n) is edge-pancyclic for each odd integer n >= 3. Moreover, TQ(n) x K(2) is also demonstrated to be geodesic 4-pancyclic. (C) 2011 Elsevier Inc. All rights reserved.
geodesic pancyclic pancyclic twisted cubes edge-pancyclic vertex-pancyclic shortest-path