Conditional edge-fault Hamiltonicity of augmented cubes

The augmented cube is a variation of hypercubes, it possesses many superior properties. In this paper, we show that, for any n-dimensional augmented cube image with faulty edges up to image in which each vertex is incident to at least two fault-free edges, there exists a fault-free Hamiltonian cycle. Our result is optimal with respect to the number of faulty edges tolerated.