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Hamiltonicity of large generalized de Bruijn cycles

Guillaume Ducoffe 1
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : In this article, we determine when the large generalized de Bruijn cycles BGC(p, d, n) are Hamiltonian. These digraphs have been introduced by Gómez, Padró and Pérennes as large interconnection networks with small diameter and they are a family of generalized p-cycles. They are the Kronecker product of the generalized de Bruijn digraph GB(d, n) and the dicycle of length p, where GB(d, n) is the digraph whose vertices are labeled with the integers modulo n such that there is an arc from vertex i to vertex j if, and only if, j ≡ di + α (mod n), for every α with 0 ≤ α ≤ d − 1.
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Guillaume Ducoffe. Hamiltonicity of large generalized de Bruijn cycles. Discrete Applied Mathematics, Elsevier, 2013, 161, pp.2200 - 2204. ⟨10.1016/j.dam.2013.02.027⟩. ⟨hal-01103786⟩

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