Fault-Tolerant Panconnectivity of Augmented Cubes AQn

The augmented cube AQ(n) is a variation of the hypercube Q(n). This paper considers the fault-tolerant Panconnectivity of AQ(n). Assume that F subset of V (AQ(n))[E(AQ(n)) and n >= 4. We prove that for any two fault-free vertices u and v with distance d in AQn, there exists a fault-free path P-uv of each length from max{d+2, 4} to 2(n) - f(v) - 1 in AQ(n) - F if vertical bar F vertical bar <= 2(n) - 4, where f(v) is the number of faulty vertices in AQ(n). Moreover, the bound is sharp.