## Abstract

A Hamiltonian cycle system of the complete graph minus a 1 factor K-2v - I (briefly, an HCS(2v)) is 2-pyramidal if it admits an automorphism group of order 2v 2 fixing two vertices. In spite of the fact that the very first example of an HCS(2v) is very old and 2-pyramidal, a thorough investigation of this class of HCSs is lacking. We give first evidence that there is a strong relationship between 2-pyramidal HCS(2v) and 1-rotational Hamiltonian cycle systems of the complete graph K2v-1. Then, as main result, we determine the full automorphism group of every 2-pyramidal HCS(2v). This allows us to obtain an exponential lower bound on the number of non-isomorphic 2-pyramidal HCS (2v).

Original language | English |
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Pages (from-to) | 747-758 |

Number of pages | 12 |

Journal | Bulletin of the Belgian Mathematical Society - Simon Stevin |

Volume | 21 |

Issue number | 4 |

Early online date | 23 Oct 2014 |

Publication status | Published - 2014 |

## Keywords

- 1-rotational Hamiltonian cycle system
- 2 pyramidal Hamiltonian cycle system
- Binary group
- Group action