Vertex-pancyclicity of augmented cubes with maximal faulty edges

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 4 to 2n, even if there are up to 2n − 3 link faults. We also show that this result is optimal.