Edge-fault-tolerant vertex-pancyclicity of augmented cubes

The n-dimensional augmented cube, denoted as AQn, a variation of the hypercube, possesses some properties superior to those of the hypercube. In this paper, we show that every vertex in AQn lies on a fault-free cycle of every length from 3 to n2, even if there are up to n−1 edge faults. We also show that our result is optimal.