Edge-fault-tolerant node-pancyclicity of twisted cubes

  • Authors:

  • Ming-Chien Yang

  • Affiliations:

  • Department of Knowledge Management, Aletheia University, Tainan County 721, Taiwan

  • Venue:
  • Information Processing Letters
  • Year:
  • 2009

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Abstract

The twisted cube is an important variant of the hypercube. Recently, Fan et al. proved that the n-dimensional twisted cube TQ"n is edge-pancyclic for every n=3. They also asked if TQ"n is edge-pancyclic with (n-3) faults for n=3. We find that TQ"n is not edge-pancyclic with only one faulty edge for any n=3. Then we prove that TQ"n is node-pancyclic with (@?n2@?-1) faulty edges for every n=3. The result is optimal in the sense that with @?n2@? faulty edges, the faulty TQ"n is not node-pancyclic for any n=3.