## 摘要

The folded hypercube FQ_{n} is a well-known variation of the hypercube structure. FQ_{n} is superior to ^{Qn} in many measurements, such as diameter, fault diameter, connectivity, and so on. Let V(FQ_{n}) (resp. E(FQ_{n})) denote the set of faulty nodes (resp. faulty edges) in FQ_{n}. In the case that all nodes in FQ _{n} are fault-free, it has been shown that FQ_{n} contains a fault-free path of length 2^{n}-1 (resp. 2^{n}-2) between any two nodes of odd (resp. even) distance if E(FQ_{n})≤n-1, where n≥1 is odd; and FQ_{n} contains a fault-free path of length 2^{n}-1 between any two nodes if E(FQ_{n})≤n-2, where n≥2 is even. In this paper, we extend the above result to obtain two further properties, which consider both node and edge faults, as follows: FQ_{n} contains a fault-free path of length at least 2^{n}-2V(FQ_{n})-1 (resp. 2^{n}-2V(FQ_{n})-2) between any two fault-free nodes of odd (resp. even) distance if V(FQ_{n})+E(FQ_{n})≤n-1, where n≥1 is odd.FQ_{n} contains a fault-free path of length at least 2^{n}-2V(FQ_{n})-1 between any two fault-free nodes if V(FQ _{n})+E(FQ_{n})≤n-2, where n≥2 is even.

原文 | English |
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頁（從 - 到） | 82-91 |

頁數 | 10 |

期刊 | Theoretical Computer Science |

卷 | 475 |

DOIs | |

出版狀態 | Published - 2013 3月 4 |

## All Science Journal Classification (ASJC) codes

- 理論電腦科學
- 一般電腦科學