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 TQn is edge-pancyclic for every n⩾3. They also asked if TQn is edge-pancyclic with (n−3) faults for n⩾3. We find that TQn is not edge-pancyclic with only one faulty edge for any n⩾3. Then we prove that TQn is node-pancyclic with faulty edges for every n⩾3. The result is optimal in the sense that with faulty edges, the faulty TQn is not node-pancyclic for any n⩾3.