Hamilton-connectivity and cycle-embedding of the Möbius cubes

The recently introduced interconnection network, the Mobius 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 Mobius cube Mn is Hamilton-connected when n ≥ 3. Then, by using the Hamilton-connectivity of Mn, we also show that any cycle of length l (4 ≤ l ≤ 2n) can be embedded into Mn with dilation 1 (n ≥ 2). It is a fact that the n-dimensional hypercube Qn does not possess these two properties.