### Abstract

A graph is k-triangular if each edge is in at least k triangles. Triangular is a synonym for 1-triangular. It is shown that the line graph of a triangular graph of order at least 4 is panconnected if and only if it is 3-connected. Furthermore, the line graph of a k-triangular graph is k-hamiltonian if and only if it is (k + 2)-connected (k ≥ 1). These results generalize work of Clark and Wormald and of Lesniak-Foster. Related results are due to Oberly and Sumner and to Kanetkar and Rao.

Original language | Undefined |
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Pages (from-to) | 399-407 |

Journal | Journal of graph theory |

Volume | 11 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1987 |

### Keywords

- IR-70828

## Cite this

Broersma, H. J., & Veldman, H. J. (1987). 3-Connected line graphs of triangular graphs are panconnected and 1-hamiltonian.

*Journal of graph theory*,*11*(3), 399-407. https://doi.org/10.1002/jgt.3190110314