Edge-bipancyclicity of the k-ary n-cubes with faulty nodes and edges |
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| Authors: | Jing Li Shiying Wang Di Liu |
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| Affiliation: | a School of Mathematical Sciences, Shanxi University, Taiyuan 030006, PR China
b Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, PR China |
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| Abstract: | The k-ary n-cube has been one of the most popular interconnection networks for massively parallel systems. In this paper, we investigate the edge-bipancyclicity of k-ary n-cubes with faulty nodes and edges. It is proved that every healthy edge of the faulty k-ary n-cube with fv faulty nodes and fe faulty edges lies in a fault-free cycle of every even length from 4 to kn − 2fv (resp. kn − fv) if k ? 4 is even (resp. k ? 3 is odd) and fv + fe ? 2n − 3. The results are optimal with respect to the number of node and edge faults tolerated. |
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| Keywords: | Interconnection networks k-Ary n-cubes Fault-tolerant Bipancyclicity Edge-bipancyclicity |
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