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 n-dimensional folded hypercube is bipartite when n is odd.We also show that the n-dimensional folded hypercube is strongly Hamiltonian-laceable when n is odd, and is Hamiltonian-connected when n = 1 or n (≥ 2) is even. c © 2007 Elsevier Ltd. All rights reserved.