### Abstract

In this paper, we focus on a hypercube-like structure, the folded hypercube, which is basically a standard hypercube with some extra links between its nodes. Let f be a faulty vertex in an n-dimensional folded hypercube F Q_{n}. We show that F Q_{n} - {f} contains a fault-free cycle of every even length from 4 to 2^{n} - 2 if n ≥ 3 and, furthermore, every odd length from n + 1 to 2^{n} - 1 if n ≥ 2 and n is even.

Original language | English |
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Pages (from-to) | 3094-3098 |

Number of pages | 5 |

Journal | Discrete Applied Mathematics |

Volume | 157 |

Issue number | 14 |

DOIs | |

Publication status | Published - 2009 Jul 28 |

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### All Science Journal Classification (ASJC) codes

- Discrete Mathematics and Combinatorics
- Applied Mathematics

### Cite this

*Discrete Applied Mathematics*,

*157*(14), 3094-3098. https://doi.org/10.1016/j.dam.2009.06.012

}

*Discrete Applied Mathematics*, vol. 157, no. 14, pp. 3094-3098. https://doi.org/10.1016/j.dam.2009.06.012

**1-vertex-fault-tolerant cycles embedding on folded hypercubes.** / Hsieh, Sun-Yuan; Kuo, Che Nan; Huang, Hui Ling.

Research output: Contribution to journal › Article

TY - JOUR

T1 - 1-vertex-fault-tolerant cycles embedding on folded hypercubes

AU - Hsieh, Sun-Yuan

AU - Kuo, Che Nan

AU - Huang, Hui Ling

PY - 2009/7/28

Y1 - 2009/7/28

N2 - In this paper, we focus on a hypercube-like structure, the folded hypercube, which is basically a standard hypercube with some extra links between its nodes. Let f be a faulty vertex in an n-dimensional folded hypercube F Qn. We show that F Qn - {f} contains a fault-free cycle of every even length from 4 to 2n - 2 if n ≥ 3 and, furthermore, every odd length from n + 1 to 2n - 1 if n ≥ 2 and n is even.

AB - In this paper, we focus on a hypercube-like structure, the folded hypercube, which is basically a standard hypercube with some extra links between its nodes. Let f be a faulty vertex in an n-dimensional folded hypercube F Qn. We show that F Qn - {f} contains a fault-free cycle of every even length from 4 to 2n - 2 if n ≥ 3 and, furthermore, every odd length from n + 1 to 2n - 1 if n ≥ 2 and n is even.

UR - http://www.scopus.com/inward/record.url?scp=67949095821&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67949095821&partnerID=8YFLogxK

U2 - 10.1016/j.dam.2009.06.012

DO - 10.1016/j.dam.2009.06.012

M3 - Article

AN - SCOPUS:67949095821

VL - 157

SP - 3094

EP - 3098

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 14

ER -