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• W2587087557 abstract "The k-ary n-cube is one of the most attractive interconnection networks for parallel and distributed computing system. In this paper, we investigate hamiltonian cycle and path embeddings in 3-ary n-cubes 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>3</sup> based on K <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1,2</sub> -structure faults, which means each faulty element is isomorphic to a connected graph K <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1,2</sub> or a connected subgraph of the connected graph. We show that for two arbitrary distinct healthy nodes of a faulty 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>3</sup> , there exists a fault-free hamiltonian path connecting these two nodes if the number of faulty element is at most n-2 and each faulty element is isomorphic to K <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1,2</sub> or a connected subgraph of K <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1,2</sub> . We also show that there exists a fault-free hamiltonian cycle if the number of faulty element is at most n-1 and each faulty element is isomorphic to K <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1,2</sub> or a connected subgraph of K <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1,2</sub> . These results mean that the 3-ary n-cube Q3n can tolerate up to 3(n - 2) faulty nodes such that 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>3</sup> - V (F) is still hamiltonian and hamiltonian-connected, where F denotes the faulty set of 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>3</sup> ." @default.
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• W2587087557 date "2016-08-01" @default.
• W2587087557 modified "2023-09-24" @default.
• W2587087557 title "Hamiltonian Cycle and Path Embeddings in 3-Ary n-Cubes Based on K1,2-Structure Faults" @default.
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• W2587087557 doi "https://doi.org/10.1109/trustcom.2016.0198" @default.
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