### Abstract

Reversing the arcs of any 3-circuit of a tournament, the score vector is unchanged; therefore the class of regular tournaments is closed under this operation. Here we prove that the number of non-isomorphic, non-symmetric tournaments obtained by reversal from a particular regular tournament on n vertices is equal to n^{2}-9/24 – 1 for n = 0 (mod 3) and n^{2}-1/24 – 2 otherwise. Moreover, we generate all the non-isomorphic regular tournaments of order 9 and present their interchange graph.

Original language | English |
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Pages (from-to) | 11-23 |

Number of pages | 13 |

Journal | Annals of Discrete Mathematics |

Volume | 52 |

Issue number | C |

DOIs | |

Publication status | Published - Jan 1 1992 |

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

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## Cite this

Astié-Vidal, A., Dugat, V., & Tuza, Z. (1992). Construction of non-isomorphic regular tournaments.

*Annals of Discrete Mathematics*,*52*(C), 11-23. https://doi.org/10.1016/S0167-5060(08)70897-5