A184953 Number of connected 5-regular (or quintic) simple graphs on 2n vertices with girth exactly 3.

0, 0, 0, 1, 3, 59, 7847, 3459376, 2585136287, 2807104844073

Offset: 0

Author

Jason Kimberley, Feb 27 2011

Keywords

• nonn
• more
• hard

Links

• Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth exactly g
• Eric Weisstein's World of Mathematics, Girth.
• Eric Weisstein's World of Mathematics, Quintic Graph.

Crossrefs

Connected k-regular simple graphs with girth exactly 3: A006923 (k=3), A184943 (k=4), this sequence (k=5), A184963 (k=6), A184973 (k=7), A184983 (k=8), A184993 (k=9).

Connected 5-regular simple graphs with girth at least g: A006821 (g=3), A058275 (g=4).

Connected 5-regular simple graphs with girth exactly g: this sequence (g=3), A184954 (g=4), A184955 (g=5).

Formula

a(n) = A006821(n) - A058275(n).