A181153 Number of connected 7-regular simple graphs on 2n vertices with girth at least 4.

1, 0, 0, 0, 0, 0, 0, 1, 1, 8, 741, 2887493

Offset: 0

Author

Jason Kimberley, last week of Jan 2011

Keywords

• nonn
• more
• hard

Comments

a(10) was computed by the author in 3 hours using GENREG on Dec 02 2009.

a(11) was computed by the author using GENREG over 45.7 processor days at U. Newcastle from Jan 25 to 27 2011.

Examples

			The a(0)=1 null graph is vacuously 7-regular and connected; since it is acyclic then it has infinite girth.
The a(7)=1 graph is the complete bipartite graph K_{7,7} on 14 vertices.
The a(8)=1 graph has girth 4, automorphism group of order 80640, and the following adjacency lists:
01 : 02 03 04 05 06 07 08
02 : 01 09 10 11 12 13 14
03 : 01 09 10 11 12 13 15
04 : 01 09 10 11 12 14 15
05 : 01 09 10 11 13 14 15
06 : 01 09 10 12 13 14 15
07 : 01 09 11 12 13 14 15
08 : 01 10 11 12 13 14 15
09 : 02 03 04 05 06 07 16
10 : 02 03 04 05 06 08 16
11 : 02 03 04 05 07 08 16
12 : 02 03 04 06 07 08 16
13 : 02 03 05 06 07 08 16
14 : 02 04 05 06 07 08 16
15 : 03 04 05 06 07 08 16
16 : 09 10 11 12 13 14 15
		

References

• M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146.

Links

• Jason Kimberley, Connected regular graphs with girth at least 4
• Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g
• M. Meringer, Tables of Regular Graphs

Crossrefs

7-regular simple graphs with girth at least 4: this sequence (connected), A185274 (disconnected), A185374 (not necessarily connected).

Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: A185114 (k=2), A014371 (k=3), A033886 (k=4), A058275 (k=5), A058276 (k=6), this sequence (k=7), A181154 (k=8), A181170 (k=9).

Connected 7-regular simple graphs with girth at least g: A014377 (g=3), this sequence (g=4).

Connected 7-regular simple graphs with girth exactly g: A184963 (g=3), A184964 (g=4).