Geodesic pancyclicity of twisted cubes

  • Authors:
  • Pao-Lien Lai

  • Affiliations:
  • Department of Computer Science and Information Engineering, National Dong Hwa University, Shoufeng, Hualien 97401, Taiwan, ROC

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

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"nxK"2 is also demonstrated to be geodesic 4-pancyclic.