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Hamilton circuits in the directed wrapped Butterfly network
, 1996
"... In this paper, we prove that the wrapped Butterfly digraph ~ WBF(d;n) of degree d and dimension n contains at least d \Gamma 1 arcdisjoint Hamilton circuits, answering a conjecture of D. Barth. We also conjecture that ~ WBF(d;n) can be decomposed into d Hamilton circuits, except for {d = 2 and n = ..."
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In this paper, we prove that the wrapped Butterfly digraph ~ WBF(d;n) of degree d and dimension n contains at least d \Gamma 1 arcdisjoint Hamilton circuits, answering a conjecture of D. Barth. We also conjecture that ~ WBF(d;n) can be decomposed into d Hamilton circuits, except for {d = 2 and n = 2}, {d = 2 and n = 3} and {d = 3 and n = 2}. We show that it suffices to prove the conjecture for d prime and n = 2. Then, we give such a Hamilton decomposition for all primes less than 12000 by a clever computer search, and so, as a corollary, we have a Hamilton decomposition of ~ WBF(d;n) for any d divisible by a number q, with 4 q 12000.
The forwarding Indices of Wrapped Butterfly Networks, Networks,DOI 10.1002/net
, 2009
"... LetG be a connected graph. A routing inG is a set of fixed paths for all ordered pairs of vertices in G. The forwarding index of G is the minimum of the largest number of paths specified by a routing passing through any vertex of G taken over all routings in G. This article investigates the forward ..."
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LetG be a connected graph. A routing inG is a set of fixed paths for all ordered pairs of vertices in G. The forwarding index of G is the minimum of the largest number of paths specified by a routing passing through any vertex of G taken over all routings in G. This article investigates the forwarding index of a wrapped butterfly graph, determines the exact value for the directed case, and gives an upper bound for undirected case. © 2008 Wiley Periodicals, Inc. NETWORKS, Vol. 00(00), 000–000 2008
Hamilton circuits in directed Butterfly networks
 RESEARCH REPORT #2925  THEME 1, INRIA SOPHIA ANTIPOLIS
, 1996
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Jl. BRI Radio Dalam No. 17 Jakarta SelatanIndonesia
"... This paper discuss about embedding on the new interconnection network named TorusButterfly. TorusButterfly is the Cartesian product network that has constant degree and has smaller network cost than the other Cartesian product network. TorusButterfly network is a Cayley graph. From the properties ..."
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This paper discuss about embedding on the new interconnection network named TorusButterfly. TorusButterfly is the Cartesian product network that has constant degree and has smaller network cost than the other Cartesian product network. TorusButterfly network is a Cayley graph. From the properties of Cayley graphs which have Hamiltonian path, the linear array and 2DMesh can be embedded into this new TorusButterfly network with minimum dilation and expansion.