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

We show that the two uni-directional n-cubes, namely UHC1_n and UHC2_n proposed by Chou and Du (1990) as interconnection schemes are Hamiltonian. In addition, we show that (1) if n is even, both architectures are vertex symmetric; and (2) if n is odd, both architectures have exactly two vertex-symmetric components. By studying symmetry, we further prove that the maximum delay of one-port one-to-all broadcasting for either architecture is at most 1.5n