### Abstract

No cubic graph has an odd number of points. A method is found of calculating the number tp of labelled connected cubic graphs with 2p points rooted at triangle. The method presupposes knowledge of the numbers qk of labelled connected cubic graphs with 2k points and k < p. Labelled connected cubic graphs have already been counted by Read, so this allows determination of the mean number tp /qp of triangles in a labelled connected cubic graph with 2p points, for all p > 1. It is shown that tp /qp → 4/3 as p →∞.

Original language | English |
---|---|

Title of host publication | Combinatorial Mathematics |

Subtitle of host publication | Proceedings of the International Conference on Combinatorial Theory Canberra, August 16-27, 1977 |

Editors | D A Holton, Jennifer Seberry |

Place of Publication | Berlin Germany |

Publisher | Springer |

Pages | 337-345 |

Number of pages | 9 |

Volume | 686 |

DOIs | |

Publication status | Published - 1978 |

Externally published | Yes |

### Publication series

Name | Lecture Notes in Mathematics |
---|---|

Publisher | Springer |

Volume | 686 |

## Cite this

Wormald, N. C. (1978). Triangles in labelled cubic graphs. In D. A. Holton, & J. Seberry (Eds.),

*Combinatorial Mathematics: Proceedings of the International Conference on Combinatorial Theory Canberra, August 16-27, 1977*(Vol. 686, pp. 337-345). (Lecture Notes in Mathematics; Vol. 686). Springer. https://doi.org/10.1007/BFb0062550