Diameter bounds of cubelike recursive networks

The cubelike recursive networks is a special sub family of the binary interconnection networks. Typical cubelike recursive networks include the hypercube, the crossed cube, the Mobius cube, the generalized twisted cube, the twisted n-cube and the twisted-cube connected network. In a general sense, lots of their topological properties and network parameters are identical, but their diameters are quite different. This work makes the following contributions: Firstly, the definitions of sub-network and super-network are introduced to explain the recursive nature on structure of the cubelike recursive networks. Secondly, the supremum and infimum of the cubelike recursive networks' diameters are n and [~(n +1)/2] respectively, which are proved according to these definitions. Finally, a routing algorithm of cubelike recursive networks is proposed, with an example presented to explain how the algorithm works.