A184974 Number of connected 7-regular simple graphs on 2n vertices with girth exactly 4.

0, 0, 0, 0, 0, 0, 0, 1, 1, 8, 741, 2887493

Offset: 0

Author

Jason Kimberley, Feb 28 2011

Keywords

• nonn
• more
• hard

Examples

			a(0)=0 because even though the null graph (on zero vertices) is vacuously 7-regular and connected, since it is acyclic, it has infinite girth.
The a(7)=1 graph is the complete bipartite graph K_{7,7}.
		

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), A184964 (k=6), this sequence (k=7).

Connected 7-regular simple graphs with girth at least g: A014377 (g=3), A181153 (g=4).

Connected 7-regular simple graphs with girth exactly g: A184973 (g=3), this sequence (g=4).

Formula

a(n) = A186714(n,5) - A186715(n,5).