# The hamiltonian index of a graph and its branch-bonds

Xiong, Liming
and
Broersma, H.J.
and
Li, Xueliang
and
Li, MingChu
(2004)
*The hamiltonian index of a graph and its branch-bonds.*
Discrete mathematics, 285
(1-3).
pp. 279-288.
ISSN 0012-365X

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Abstract: | Let G be an undirected and loopless finite graph that is not a path. The smallest integer m such that the iterated line graph Lm(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) ≤ 2 is given here. We use it to establish a sharp lower bound and a sharp upper bound on h(G), respectively, thereby improving some known results of Catlin et al. [J. Graph Theory 14 (1990) 347] and Hong-Jian Lai [Discrete Math. 69 (1988) 43]. Examples show that h(G) may reach all integers between the lower bound and the upper bound. We also propose some questions on the topic. |

Item Type: | Article |

Copyright: | © 2004 Elsevier |

Faculty: | Electrical Engineering, Mathematics and Computer Science (EEMCS) |

Research Group: | |

Link to this item: | http://purl.utwente.nl/publications/75735 |

Official URL: | https://doi.org/10.1016/j.disc.2004.01.018 |

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Metis ID: 220324