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• W2078021104 abstract "The k-ary n-cube Q <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>k</sup> n is one of the most attractive interconnection networks for parallel and distributed systems. In this paper, we consider the problem of a fault-free hamiltonian cycle passing through prescribed edges in a k-ary n-cube Q <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>k</sup> with some faulty edges. The following result is obtained: For any n ≥ 2 and k ≥ 3, let F ⊂ E(Q <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>k</sup> ), P ⊂ E(Q <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>k</sup> ) F with |P|≤ 2n - 2, |F| ≤ 2n - (|P| + 2). Then there exists a hamiltonian cycle passing through all edges of P in Q <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>n</sub> <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>k</sup> - F if and only if the subgraph induced by P consists of pairwise vertex-disjoint paths. It improves the result given by Yang and Wang [34]." @default.
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• W2078021104 date "2015-02-01" @default.
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• W2078021104 title "Fault-Free Hamiltonian Cycles Passing through Prescribed Edges in <formula formulatype=inline><tex Notation=TeX>$k$</tex> <mathgraphic graphicformat=GIF fileref=zhang-ieq1-2311794.gif/></formula>-Ary <formula formulatype=inline><tex Notation=TeX> $n$</tex><mathgraphic graphicformat=GIF fileref=zhang-ieq2-2311794.gif/></formula>-Cubes with Faulty Edges" @default.
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• W2078021104 doi "https://doi.org/10.1109/tpds.2014.2311794" @default.
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