The following tables contain numbers of connected regular multigraphs. They were computed with a graph generator written by Thomas Grüner. Planarity testing was done by an algorithm which is included in the EWS.

The following table contains numbers of connected regular multigraphs with given number of vertices and degree. For the empty fields the number is not yet known (to me).

Vertices | Degree 3 | Degree 4 | Degree 5 |
---|---|---|---|

2 | 1 | ||

3 | 0 | ||

4 | 2 | ||

5 | 0 | ||

6 | 6 | ||

7 | 0 | ||

8 | 20 | ||

9 | 0 | ||

10 | 91 | ||

11 | 0 | ||

12 | 509 | ||

13 | 0 | ||

14 | 3608 | ||

15 | 0 | ||

16 | 31856 | ||

17 | 0 | ||

18 | 340416 | ||

19 | 0 | ||

20 | 4269971 |

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The following table contains numbers of connected planar regular multigraphs with given number of vertices and degree. For the empty fields the number is not yet known (to me).

Vertices | Degree 3 | Degree 4 | Degree 5 |
---|---|---|---|

2 | 1 | ||

3 | 0 | ||

4 | 2 | ||

5 | 0 | ||

6 | 5 | ||

7 | 0 | ||

8 | 17 | ||

9 | 0 | ||

10 | 71 | ||

11 | 0 | ||

12 | 357 | ||

13 | 0 | ||

14 | 2143 | ||

15 | 0 | ||

16 | 14958 | ||

17 | 0 | ||

18 | 116526 | ||

19 | 0 | ||

20 | 986540 |

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Markus Meringer, November 1997