Hamilton-connectivity and cycle-embedding of the Möbius cubes

The recently introduced interconnection network, the Möbius cube, is an important variant of the hypercube. This network has several attractive properties compared with the hypercube. In this paper, we show that the n-dimensional Möbius cube M_n is Hamilton-connected when n?3. Then, by using the Hamilton-connectivity of M_n, we also show that any cycle of length l (4?l?2ⁿ) can be embedded into M_n with dilation 1 (n?2). It is a fact that the n-dimensional hypercube Q_n does not possess these two properties.