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 (n?3) ( n ? 3 ) with faulty edges up to 4n-8 4 n - 8 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.
hamiltonicity augmented cubes hamiltonian cycles fault-tolerant embedding graph-theoretic interconnection networks