This page contains graphs and counts of various planar graph classes. All of these graphs and numbers were obtained by the program plantri, except the counts for connected planar graphs which were obtained by the program geng.

The graph lists available in 'planar_code' or 'graph6' format. The larger files are compressed with gzip.

The following lists are available:

- Connected planar graphs
- 3-connected planar triangulations
- 3-connected planar triangulations of a disk
- 3-connected planar simple graphs (i.e. convex polytopes)
- 3-connected planar quadrangulations

For fullerenes, see the Fullerenes page.

Some additional lists of planar graphs can be found on Brendan McKay's planar graph page.

Plantri can generate much more graph classes than the ones listed on this page (e.g. planar graphs with a given minimum degree or with connectivity requirements). For a complete list of the graph classes which can be generated with this program, see the plantri page.

The table below lists the number of non-isomorphic connected planar graphs. Note that isomorphism is considered according to the abstract graphs regardless of their embedding. So graphs which can be embedded in multiple ways only appear once in the lists. If you are looking for plane graphs which are not isomorphic as embedded graphs, we refer to the plantri-page.

Vertices | No. of graphs |
---|---|

1 | 1 |

2 | 1 |

3 | 2 |

4 | 6 |

5 | 20 |

6 | 99 |

7 | 646 |

8 | 5974 |

9 | 71885 |

10 | 1052805 |

11 | 17449299 |

12 | 313372298 |

Note that the dual graph of a 3-connected planar triangulation is a cubic polyhedron (i.e. a cubic 3-connected simple planar graph).

Vertices | No. of graphs |
---|---|

4 | 1 |

5 | 1 |

6 | 2 |

7 | 5 |

8 | 14 |

9 | 50 |

10 | 233 |

11 | 1249 |

12 | 7595 |

13 | 49566 |

14 | 339722 |

15 | 2406841 |

16 | 17490241 |

17 | 129664753 |

18 | 977526957 |

19 | 7475907149 |

20 | 57896349553 |

21 | 453382272049 |

22 | 3585853662949 |

23 | 28615703421545 |

Vertices | No. of graphs |
---|---|

4 | 1 |

5 | 2 |

6 | 7 |

7 | 27 |

8 | 132 |

9 | 773 |

10 | 5017 |

11 | 34861 |

12 | 253676 |

13 | 1903584 |

14 | 14616442 |

15 | 114254053 |

16 | 906266345 |

17 | 7277665889 |

18 | 59066524810 |

19 | 483864411124 |

20 | 3996427278475 |

21 | 33250623548406 |

Vertices | No. of graphs |
---|---|

4 | 1 |

5 | 2 |

6 | 7 |

7 | 34 |

8 | 257 |

9 | 2606 |

10 | 32300 |

11 | 440564 |

12 | 6384634 |

13 | 96262938 |

14 | 1496225352 |

15 | 23833988129 |

16 | 387591510244 |

17 | 6415851530241 |

18 | 107854282197058 |

Vertices | No. of graphs |
---|---|

8 | 1 |

9 | 0 |

10 | 1 |

11 | 1 |

12 | 3 |

13 | 3 |

14 | 11 |

15 | 18 |

16 | 58 |

17 | 139 |

18 | 451 |

19 | 1326 |

20 | 4461 |

21 | 14554 |

22 | 49957 |

23 | 171159 |

24 | 598102 |

25 | 2098675 |

26 | 7437910 |

27 | 26490072 |

28 | 94944685 |

29 | 341867921 |

30 | 1236864842 |

31 | 4493270976 |

32 | 16387852863 |

33 | 59985464681 |

34 | 220320405895 |

35 | 811796327750 |

36 | 3000183106119 |