## Abstract

We consider fault-tolerant embedding, where an-dimensional faulty hypercube, denoted by Q_{n}, acts as the host graph, and the longest fault-free cycle represents the guest graph. Let F_{v} be a set of faulty nodes in Q_{n}. Also, let F_{e} be a set of faulty edges in which at least one end-node of each edge is faulty, and let F_{e} be a set of faulty edges in which the end-nodes of each edge are both fault-free. An edge Q_{n} in is said to be critical if it is either fault-free or in F_{e}. In this paper, we prove that there exists a fault-free cycle of length at least 2^{n}-2|F_{v}| in Q_{n} (n≥3) with |F_{e}| ≤ 2n-5, and |F_{v}|+|F_{e}|≤2n-4, in which each node is incident to at least two critical edges. Our result improves on the previously best known results reported in the literature, where only faulty nodes or faulty edges are considered.

Original language | English |
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Article number | 5332283 |

Pages (from-to) | 702-710 |

Number of pages | 9 |

Journal | IEEE Transactions on Reliability |

Volume | 58 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2009 Nov 16 |

## All Science Journal Classification (ASJC) codes

- Safety, Risk, Reliability and Quality
- Electrical and Electronic Engineering