### Abstract

A bipartite graph is hamiltonian laceable if there exists a hamiltonian path between any two vertices that are in different partite sets. A hamiltonian laceable graph G is said to be hyper-hamiltonian laceable if, for any vertex v of G, there exists a hamiltonian path of G - {v} joining any two vertices that are located in the same partite set different from that of v. In this paper, we further improve the hyper-hamiltonian laceability of hypercubes by showing that, for any two vertices x, y from one partite set of Q(n), n >= 4, and any vertex w from the other partite set, there exists a hamiltonian path H of Q(n) - {w} joining x to y such that d(H)(X, Z) = l for any vertex z is an element of V(Q(n)) - {x, y, w} and for every integer l satisfying both d(Qn) (x, z) <= l <= 2(n) - 2 - d(Qn) (z, y) and 2 vertical bar(l - d(Qn) (x, z)). As a consequence, many attractive properties of hypercubes follow directly from our result.

Original language | English |
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Title of host publication | CEA'09: PROCEEDINGS OF THE 3RD WSEAS INTERNATIONAL CONFERENCE ON COMPUTER ENGINEERING AND APPLICATIONS |

Editors | L Xi |

Pages | 62-+ |

State | Published - 2009 |

Event | 3rd WSEAS International Conference on Computer Engineering and Applications - Ningbo, PEOPLES R CHINA, Ningbo, China Duration: 10 Jan 2009 → 12 Jan 2009 |

### Publication series

Name | Electrical and Computer Engineering Series |
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### Conference

Conference | 3rd WSEAS International Conference on Computer Engineering and Applications |
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Country | China |

City | Ningbo |

Period | 10/01/09 → 12/01/09 |

### Keywords

- Path embedding; Hamiltonian laceable; Hyper-hamiltonian laceable; Interconnection network; Hypercube

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## Cite this

Tsai, T. H., Kung, T-L., Tan, J-M., & Hsu, L. H. (2009). On the Enhanced Hyper-hamiltonian Laceability of Hypercubes. In L. Xi (Ed.),

*CEA'09: PROCEEDINGS OF THE 3RD WSEAS INTERNATIONAL CONFERENCE ON COMPUTER ENGINEERING AND APPLICATIONS*(pp. 62-+). (Electrical and Computer Engineering Series).