Geodesic
Embeddings of hamiltonian paths in faulty k-ary 2-cubes
Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 1, pp. 47-61

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It is well known that the k-ary n-cube has been one of the most efficient interconnection networks for distributed-memory parallel systems. A k-ary n-cube is bipartite if and only if k is even. Let (X,Y) be a bipartition of a k-ary 2-cube (even integer k ≥ 4). In this paper, we prove that for any two healthy vertices u ∈ X, v ∈ Y, there exists a hamiltonian path from u to v in the faulty k-ary 2-cube with one faulty vertex in each part.
Keywords: complex networks, path embeddings, fault-tolerance, k-ary n-cubes 
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Wang, Shiying; Zhang, Shurong. Embeddings of hamiltonian paths in faulty k-ary 2-cubes. Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 1, pp. 47-61. http://geodesic.mathdoc.fr/item/DMGT_2012_32_1_a4/