A *cograph* or complement-reducible graph is a graph that can be generated from the single-vertex graph *K _{1}* by complementation and disjoint union.
An alternative and equivalent characterisation is that the class of

Below are the lists of connected cographs. These graphs were generated by Átila Jones using the generation algorithm described in [1]. The source code of this algorithm can be found here. The graph lists are currently only available in 'graph6' format. The larger files are compressed with gzip.

Vertices | No. of cographs |
---|---|

1 | 1 |

2 | 1 |

3 | 2 |

4 | 5 |

5 | 12 |

6 | 33 |

7 | 90 |

8 | 261 |

9 | 766 |

10 | 2312 |

11 | 7068 |

12 | 21965 |

13 | 68954 |

14 | 218751 |

15 | 699534 |

16 | 2253676 |

17 | 7305788 |

18 | 23816743 |

19 | 78023602 |

20 | 256738751 |

21 | 848152864 |

22 | 2811996972 |

23 | 9353366564 |

24 | 31204088381 |

25 | 104384620070 |

26 | 350064856815 |

27 | 1176693361956 |

28 | 3963752002320 |

[1] A.A. Jones, F. Protti and R.R. Del-Vecchio, Cograph generation with linear delay, Theoretical Computer Science, 713:1-10, 2018.