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A181154
Number of connected 8-regular simple graphs on n vertices with girth at least 4.
13
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.
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
KEYWORD
nonn,more,hard
AUTHOR
Jason Kimberley, week to Jan 31 2011
STATUS
approved