Edge-fault-tolerant node-pancyclicity of twisted cubes

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 TQn is node-pancyclic with ([n/2] - 1) faulty edges for every n >= 3. The result is optimal in the sense that with [n/2] faulty edges, the faulty TQ(n) is not node-pancyclic for any n >= 3. (C) 2009 Elsevier B.V. All rights reserved.