A184964 Number of connected 6-regular simple graphs on n vertices with girth exactly 4.

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

Author

Jason Kimberley, Feb 28 2011

Keywords

• nonn
• hard
• more

Comments

Other than at n=0, this sequence first differs from A058276 at n = A054760(6,5) = 40.

Examples

			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}.
		

Links

• Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth exactly g

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).