Abstract
The twisted cube is an important variant of the hypercube. Recently, Fan et al. proved that the n-dimensional twisted cube T Q n is edge-pancyclic for every n ⩾ 3 . They also asked if T Q n is edge-pancyclic with ( n − 3 ) faults for n ⩾ 3 . We find that T Q n is not edge-pancyclic with only one faulty edge for any n ⩾ 3 . Then we prove that T Q n 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 T Q n is not node-pancyclic for any n ⩾ 3 .
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