### Abstract

Original language | Undefined |
---|---|

Place of Publication | Enschede |

Publisher | University of Twente |

Number of pages | 13 |

Publication status | Published - 2001 |

### Publication series

Name | Memorandum Faculteit TW |
---|---|

Publisher | University of Twente |

No. | 1611 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-05C35
- EWI-3431
- MSC-05C45
- METIS-203117
- IR-65798

### Cite this

*The Hamiltonian index of a graph and its branch-bonds*. (Memorandum Faculteit TW; No. 1611). Enschede: University of Twente.

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*The Hamiltonian index of a graph and its branch-bonds*. Memorandum Faculteit TW, no. 1611, University of Twente, Enschede.

**The Hamiltonian index of a graph and its branch-bonds.** / Xiong, L.; Liming, X.; Broersma, Haitze J.; Li, X.; Li, Xueliang.

Research output: Book/Report › Report › Professional

TY - BOOK

T1 - The Hamiltonian index of a graph and its branch-bonds

AU - Xiong, L.

AU - Liming, X.

AU - Broersma, Haitze J.

AU - Li, X.

AU - Li, Xueliang

N1 - Imported from MEMORANDA

PY - 2001

Y1 - 2001

N2 - Let $G$ be an undirected and loopless finite graph that is not a path. The minimum $m$ such that the iterated line graph $L^m(G)$ is hamiltonian is called the hamiltonian index of $G,$ denoted by $h(G).$ A reduction method to determine the hamiltonian index of a graph $G$ with $h(G)\geq 2$ is given here. With it we will establish a sharp lower bound and a sharp upper bound for $h(G)$, respectively, which improves some known results of P.A. Catlin et al. [J. Graph Theory 14 (1990)] and H.-J. Lai [Discrete Mathematics 69 (1988)]. Examples show that $h(G)$ may reach all integers between the lower bound and the upper bound.

AB - Let $G$ be an undirected and loopless finite graph that is not a path. The minimum $m$ such that the iterated line graph $L^m(G)$ is hamiltonian is called the hamiltonian index of $G,$ denoted by $h(G).$ A reduction method to determine the hamiltonian index of a graph $G$ with $h(G)\geq 2$ is given here. With it we will establish a sharp lower bound and a sharp upper bound for $h(G)$, respectively, which improves some known results of P.A. Catlin et al. [J. Graph Theory 14 (1990)] and H.-J. Lai [Discrete Mathematics 69 (1988)]. Examples show that $h(G)$ may reach all integers between the lower bound and the upper bound.

KW - MSC-05C35

KW - EWI-3431

KW - MSC-05C45

KW - METIS-203117

KW - IR-65798

M3 - Report

T3 - Memorandum Faculteit TW

BT - The Hamiltonian index of a graph and its branch-bonds

PB - University of Twente

CY - Enschede

ER -