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A184945
Number of connected 4-regular simple graphs on n vertices with girth exactly 5.
12
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 8, 131, 3917, 123859, 4131991, 132160607, 4018022149, 118369811959
OFFSET
0,21
FORMULA
a(n) = A058343(n) - A058348(n).
EXAMPLE
a(0)=0 because even though the null graph (on zero vertices) is vacuously 4-regular and connected, since it is acyclic, it has infinite girth.
The a(19)=1 graph is the unique (4,5) cage: the Robertson graph (see also A159191). It has the following adjacency lists.
01 : 02 03 04 05
02 : 01 06 07 08
03 : 01 09 10 11
04 : 01 12 13 14
05 : 01 15 16 17
06 : 02 09 12 15
07 : 02 10 13 16
08 : 02 11 14 17
09 : 03 06 13 17
10 : 03 07 14 18
11 : 03 08 16 19
12 : 04 06 16 18
13 : 04 07 09 19
14 : 04 08 10 15
15 : 05 06 14 19
16 : 05 07 11 12
17 : 05 08 09 18
18 : 10 12 17 19
19 : 11 13 15 18
CROSSREFS
4-regular simple graphs with girth exactly 5: this sequence (connected), A185045 (disconnected), A185145 (not necessarily connected).
Connected k-regular simple graphs with girth exactly 5: A006925 (k=3), this sequence (k=4), A184955 (k=5).
Connected 4-regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), A058343 (g=5), A058348 (g=6).
Connected 4-regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), this sequence (g=5).
Sequence in context: A178173 A058891 A274171 * A058343 A267407 A337296
KEYWORD
nonn,hard,more
AUTHOR
Jason Kimberley, Feb 14 2011
STATUS
approved