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Generalized shuffle-exchange digraphs: Hamiltonian properties

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3 Author(s)
Hongfang Liu ; Div. of Comput. Sci., City Univ. of New York, NY, USA ; Hsu, D.F. ; Horiguchi, S.

The k-ary n-dimensional shuffle-exchange directed network S(k, n) consists of kn nodes such that each node is represented as an k-ary n-tuple vector, a1a2...an, where ai is in [0, k-1]. Node a1a2...an is adjacent to node a2a3...ana 1 (one shuffle link) and k-1 other nodes a1a2 ...an-1b, where b∈[0, k-1] and b≠an (k-1 exchange links). S(k, n) have been widely used as topologies for VLSI networks, parallel architectures, and communication systems. However, since S(k, n) does not exist for the number of nodes between k n and kn+1, Liu and Hsu have recently proposed a class of digraphs GS(k, N), which generalized S(k, n) to any number N of nodes. They also showed that GS(k, N) retains all the nice properties of S(k, n). In this paper, we survey these combinatorial properties and study Hamiltonian properties of GS(k, N). In particular, we have successfully obtained a Hamiltonian circuit for GS(k, k(k+1)) for any k>2

Published in:

Circuits and Systems, 1999. ISCAS '99. Proceedings of the 1999 IEEE International Symposium on  (Volume:6 )

Date of Conference:

Jul 1999

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