A181154 Number of connected 8-regular simple graphs on n vertices with girth at least 4.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 13, 1

Offset

0,21

Comments

a(20) and a(21) were computed by the author, using GENREG, over 79 processor hours and 294 processor days, respectively, during Dec 2009.

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..21.

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 8-regular and connected; since it is acyclic then it has infinite girth.
The a(16)=1 graph is the complete bipartite graph K_{8,8}.
The a(21)=1 graph has girth 4, automorphism group of order 829440, and the following adjacency lists:
01 : 02 03 04 05 06 07 08 09
02 : 01 10 11 12 13 14 15 16
03 : 01 10 11 12 13 14 15 16
04 : 01 10 11 12 13 14 15 16
05 : 01 10 11 12 13 14 15 16
06 : 01 10 11 12 17 18 19 20
07 : 01 10 11 13 17 18 19 20
08 : 01 10 12 13 17 18 19 20
09 : 01 11 12 13 17 18 19 20
10 : 02 03 04 05 06 07 08 21
11 : 02 03 04 05 06 07 09 21
12 : 02 03 04 05 06 08 09 21
13 : 02 03 04 05 07 08 09 21
14 : 02 03 04 05 17 18 19 20
15 : 02 03 04 05 17 18 19 20
16 : 02 03 04 05 17 18 19 20
17 : 06 07 08 09 14 15 16 21
18 : 06 07 08 09 14 15 16 21
19 : 06 07 08 09 14 15 16 21
20 : 06 07 08 09 14 15 16 21
21 : 10 11 12 13 17 18 19 20

Crossrefs

8-regular simple graphs with girth at least 4: this sequence (connected), A185284 (disconnected), A185384 (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), A181153 (k=7), this sequence (k=8), A181170 (k=9).

Connected 8-regular simple graphs with girth at least g: A184981 (triangle); chosen g: A014378 (g=3), this sequence (g=4).

Connected 8-regular simple graphs with girth exactly g: A184980 (triangle); chosen g: A184983 (g=3).

Sequence in context: A096069 A180265 A165400 * A367303 A357912 A251072

Adjacent sequences: A181151 A181152 A181153 * A181155 A181156 A181157

Keyword

nonn,more,hard

Author

Jason Kimberley, week to Jan 31 2011

Status

approved