A181170 Number of connected 9-regular simple graphs on 2n vertices with girth at least 4.

1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 14

Offset

0,12

Comments

a(11)=14 was computed by the author using GENREG at U. Ncle. over 615 processor days during Dec 2009.

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

M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146.

Example

The a(0)=1 null graph is vacuously 8-regular and connected; since it is acyclic then it has infinite girth.
The a(9)=1 graph is the complete bipartite graph K_{9,9} with 18 vertices.
The a(10)=1 graph has girth 4, automorphism group of order 7257600, and the following adjacency lists:
01 : 02 03 04 05 06 07 08 09 10
02 : 01 11 12 13 14 15 16 17 18
03 : 01 11 12 13 14 15 16 17 19
04 : 01 11 12 13 14 15 16 18 19
05 : 01 11 12 13 14 15 17 18 19
06 : 01 11 12 13 14 16 17 18 19
07 : 01 11 12 13 15 16 17 18 19
08 : 01 11 12 14 15 16 17 18 19
09 : 01 11 13 14 15 16 17 18 19
10 : 01 12 13 14 15 16 17 18 19
11 : 02 03 04 05 06 07 08 09 20
12 : 02 03 04 05 06 07 08 10 20
13 : 02 03 04 05 06 07 09 10 20
14 : 02 03 04 05 06 08 09 10 20
15 : 02 03 04 05 07 08 09 10 20
16 : 02 03 04 06 07 08 09 10 20
17 : 02 03 05 06 07 08 09 10 20
18 : 02 04 05 06 07 08 09 10 20
19 : 03 04 05 06 07 08 09 10 20
20 : 11 12 13 14 15 16 17 18 19

Crossrefs

9-regular simple graphs with girth at least 4: this sequence (connected), A185294 (disconnected).

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), A181153 (k=7), A181154 (k=8), this sequence (k=9).

Connected 9-regular simple graphs with girth at least g: A014378 (g=3), this sequence (g=4).

Connected 9-regular simple graphs with girth exactly g: A184993 (g=3).

Sequence in context: A228033 A102910 A262298 * A243830 A002337 A008423

Adjacent sequences: A181167 A181168 A181169 * A181171 A181172 A181173

Keyword

nonn,more,hard

Author

Jason Kimberley, last week of Jan 2011

Status

approved