### Abstract

Let F be a set of f <= 2n - 5 faulty nodes in an n-cube Q(n) such that every node of Q(n) still has at least two fault-free neighbors. Then we show that Q(n) - F contains a path of length at least 2(n) - 2f - 1 (respectively, 2(n) - 2f - 2) between any two nodes of odd (respectively, even) distance. Since the n-cube is bipartite, the path of length 2(n) - 2f - 1 (or 2(n) - 2f - 2) turns out to be the longest if all faulty nodes belong to the same partite set. As a contribution, our study improves upon the previous result presented by [J.-S. Fu, Longest fault-free paths in hypercubes with vertex faults, Information Sciences 176 (2006) 759-771] where only n - 2 faulty nodes are considered. (c) 2008 Elsevier Inc. All rights reserved.

Original language | English |
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Pages (from-to) | 667-681 |

Number of pages | 15 |

Journal | Information Sciences |

Volume | 179 |

Issue number | 5 |

DOIs | |

State | Published - 15 Feb 2009 |

### Keywords

- Interconnection network; Hypercube; Fault tolerance; Conditional fault; Linear array; Path embedding

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## Cite this

Kueng, T-L., Liang, T., Hsu, L. H., & Tan, J-M. (2009). Long paths in hypercubes with conditional node-faults.

*Information Sciences*,*179*(5), 667-681. https://doi.org/10.1016/j.ins.2008.10.015