Hamiltonicity, vertex symmetry, and broadcasting of uni-directional hypercubes

The authors show that the two uni-directional hypercubes, namely UHCl_n and UHC2_n, proposed by Chou and Du (1990) as interconnection schemes, are Hamiltonian. In addition, the authors show that if n is even: both architectures are vertex symmetric, and that if n is odd, both architectures have exactly two vertex-symmetric components. Furthermore, the study of the symmetry leads to an effective analysis of the maximum delay of one-port one-to-all broadcasting for either architecture which is at most [1.5n]