Hamiltonian-connectivity and strongly Hamiltonian-laceability of folded hypercubes

In this paper, we analyze a hypercube-like structure, called the folded hypercube, which is basically a standard hypercube with some extra links established between its nodes. We first show that the nn-dimensional folded hypercube is bipartite when nn is odd. We also show that the nn-dimensional folded hypercube is strongly Hamiltonian-laceable when nn is odd, and is Hamiltonian-connected when n=1n=1 or n(≥2) is even.