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A186729
Number of connected regular simple graphs on n vertices with girth at least 9.
10
1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19
OFFSET
0,59
EXAMPLE
The null graph is vacuously regular; there is one 0-regular simple graph with 1 vertex, and one 1-regular simple graph with 2 vertices; each of those three graphs, being acyclic, has infinite girth.
The n-cycle is the connected 2-regular graph with girth n.
The (3,9)-cages have order 58 and there are 18 of them.
CROSSREFS
Connected regular graphs of any degree with girth at least g: A005177 (g=3), A186724 (g=4), A186725 (g=5), A186726 (g=6), A186727 (g=7), A186728 (g=8), this sequence (g=9).
Connected k-regular simple graphs with girth at least 9: this sequence (all k), A186719 (triangular array), A185119 (k=2).
Sequence in context: A013886 A259327 A271975 * A340650 A226373 A240952
KEYWORD
nonn,hard,more
AUTHOR
Jason Kimberley, Oct 22 2011
STATUS
approved