Regular Multigraphs

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.

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Connected regular multigraphs

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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Connected planar regular multigraphs

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