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A184964
Number of connected 6-regular simple graphs on n vertices with girth exactly 4.
11
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 9, 6, 267, 3727, 483012, 69823723, 14836130862
OFFSET
0,17
COMMENTS
Other than at n=0, this sequence first differs from A058276 at n = A054760(6,5) = 40.
EXAMPLE
a(0)=0 because even though the null graph (on zero vertices) is vacuously 6-regular and connected, since it is acyclic, it has infinite girth.
The a(12)=1 graph is the complete bipartite graph K_{6,6}.
CROSSREFS
Connected k-regular simple graphs with girth exactly 4: A006924 (k=3), A184944 (k=4), A184954 (k=5), this sequence (k=6), A184974 (k=7).
Connected 6-regular simple graphs with girth at least g: A006822 (g=3), A058276 (g=4).
Connected 6-regular simple graphs with girth exactly g: A184963 (g=3), this sequence (g=4).
Sequence in context: A370151 A038296 A058276 * A185364 A085678 A256687
KEYWORD
nonn,hard,more
AUTHOR
Jason Kimberley, Feb 28 2011
STATUS
approved