The Edge-Fault-Tolerant Hamiltonian Connectivity of Enhanced Hypercube

In this article, we analyze the edge-fault-tolerant properties of the enhanced hypercube, which is an attractive variant of hypercube and is obtained by adding some complementary edges from hypercube. We show that an n-dimensional enhanced hypercube Qn,k(1≤ k ≤ n-1) is (n - 2)-edge-fault-tolerant Hamiltonian-connected when n(≥ 2) and k have the different parity.