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

0,10

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.

References

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

Links

Table of n, a(n) for n=0..11.

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

Example

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

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).

Sequence in context: A254857 A058921 A240283 * A184974 A060183 A262353

Adjacent sequences: A181150 A181151 A181152 * A181154 A181155 A181156

Keyword

nonn,more,hard

Author

Jason Kimberley, last week of Jan 2011

Status

approved