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Cyclic-Cubes: A New Family of Interconnection Networks of Even Fixed-Degrees
December 1998 (vol. 9 no. 12)
pp. 1253-1268

Abstract—We introduce a new family of interconnection networks that are Cayley graphs with fixed degrees of any even number greater than or equal to four. We call the proposed graphs cyclic-cubes because contracting some cycles in such a graph results in a generalized hypercube. These Cayley graphs have optimal fault tolerance and logarithmic diameters. For comparable number of nodes, a cyclic-cube can have a diameter smaller than previously known fixed-degree networks. The proposed graphs can adopt an optimum routing algorithm known for one of its subfamilies of Cayley graphs. We also show that a graph in the new family has a Hamiltonian cycle and, hence, there is an embedding of a ring. Embedding of meshes and hypercubes are also discussed.

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Index Terms:
Cayley graphs, generalized hypercube, fixed degree, interconnection.
Ada Wai-chee Fu, Siu-Cheung Chau, "Cyclic-Cubes: A New Family of Interconnection Networks of Even Fixed-Degrees," IEEE Transactions on Parallel and Distributed Systems, vol. 9, no. 12, pp. 1253-1268, Dec. 1998, doi:10.1109/71.737700
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