A186729 Number of connected regular simple graphs on n vertices with girth at least 9.

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

Author

Jason Kimberley, Oct 22 2011

Keywords

• nonn
• hard
• more

Examples

			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.
		

Links

• Andries E. Brouwer, Cages
• House of Graphs, Cubic graphs
• Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

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).