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

Authors:
Shyh-Chain Chern;Tai-Ching Tuan;Jung-Sing Jwo
Affiliations:
-;-;-
Venue:
PAS '95 Proceedings of the First Aizu International Symposium on Parallel Algorithms/Architecture Synthesis
Year:
1995

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Abstract

We show that the two uni-directional n-cubes, namely UHC1/sub n/ and UHC2/sub 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.