### Abstract

The hamiltonian index of a graph $G$ is the smallest integer $k$ such that the $k$-th iterated line graph of $G$ is hamiltonian. We first show that, with one exceptional case, adding an edge to a graph cannot increase its hamiltonian index. We use this result to prove that neither the contraction of an $A_G(F)$-contractible subgraph $F$ of a graph $G$ nor the closure operation performed on $G$ (if $G$ is claw-free) affects the value of the hamiltonian index of a graph $G$.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 2002 |

### Publication series

Name | Memorandum |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1622 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-05C45
- IR-65809
- EWI-3442
- MSC-05C35

## Cite this

Xiong, L., Ryjáček, Z., & Broersma, H. J. (2002).

*On stability of the Hamiltonian index under contractions and closures*. (Memorandum; No. 1622). Enschede: University of Twente, Department of Applied Mathematics.