### Abstract

The k-ary n-cube, denoted by Q_{n}^{k}, is one of the most important interconnection networks for parallel computing. In this paper, we consider the problem of embedding cycles and paths into faulty 3-ary n-cubes. Let F be a set of faulty nodes and/or edges, and n ≥ 2. We show that when | F | ≤ 2 n - 2, there exists a cycle of any length from 3 to | V (Q_{n}^{3} - F) | in Q_{n}^{3} - F. We also prove that when | F | ≤ 2 n - 3, there exists a path of any length from 2 n - 1 to | V (Q_{n}^{3} - F) | - 1 between two arbitrary nodes in Q_{n}^{3} - F. Since the k-ary n-cube is regular of degree 2 n, the fault-tolerant degrees 2 n - 2 and 2 n - 3 are optimal.

Original language | English |
---|---|

Pages (from-to) | 198-208 |

Number of pages | 11 |

Journal | Information Sciences |

Volume | 180 |

Issue number | 1 |

DOIs | |

State | Published - 2 Jan 2010 |

### Fingerprint

### Keywords

- Cycle
- Embedding
- Fault-tolerance
- Interconnection networks
- Path
- k-Ary n-cube

### Cite this

*Information Sciences*,

*180*(1), 198-208. https://doi.org/10.1016/j.ins.2009.09.002

}

*Information Sciences*, vol. 180, no. 1, pp. 198-208. https://doi.org/10.1016/j.ins.2009.09.002

**Embedding paths and cycles in 3-ary n-cubes with faulty nodes and links.** / Dong, Qiang; Yang, Xiaofan; Wang, Dajin.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Embedding paths and cycles in 3-ary n-cubes with faulty nodes and links

AU - Dong, Qiang

AU - Yang, Xiaofan

AU - Wang, Dajin

PY - 2010/1/2

Y1 - 2010/1/2

N2 - The k-ary n-cube, denoted by Qnk, is one of the most important interconnection networks for parallel computing. In this paper, we consider the problem of embedding cycles and paths into faulty 3-ary n-cubes. Let F be a set of faulty nodes and/or edges, and n ≥ 2. We show that when | F | ≤ 2 n - 2, there exists a cycle of any length from 3 to | V (Qn3 - F) | in Qn3 - F. We also prove that when | F | ≤ 2 n - 3, there exists a path of any length from 2 n - 1 to | V (Qn3 - F) | - 1 between two arbitrary nodes in Qn3 - F. Since the k-ary n-cube is regular of degree 2 n, the fault-tolerant degrees 2 n - 2 and 2 n - 3 are optimal.

AB - The k-ary n-cube, denoted by Qnk, is one of the most important interconnection networks for parallel computing. In this paper, we consider the problem of embedding cycles and paths into faulty 3-ary n-cubes. Let F be a set of faulty nodes and/or edges, and n ≥ 2. We show that when | F | ≤ 2 n - 2, there exists a cycle of any length from 3 to | V (Qn3 - F) | in Qn3 - F. We also prove that when | F | ≤ 2 n - 3, there exists a path of any length from 2 n - 1 to | V (Qn3 - F) | - 1 between two arbitrary nodes in Qn3 - F. Since the k-ary n-cube is regular of degree 2 n, the fault-tolerant degrees 2 n - 2 and 2 n - 3 are optimal.

KW - Cycle

KW - Embedding

KW - Fault-tolerance

KW - Interconnection networks

KW - Path

KW - k-Ary n-cube

UR - http://www.scopus.com/inward/record.url?scp=70350571716&partnerID=8YFLogxK

U2 - 10.1016/j.ins.2009.09.002

DO - 10.1016/j.ins.2009.09.002

M3 - Article

VL - 180

SP - 198

EP - 208

JO - Information Sciences

JF - Information Sciences

SN - 0020-0255

IS - 1

ER -