A165655 Number of disconnected 5-regular (quintic) graphs on 2n vertices.

0, 0, 0, 0, 0, 0, 1, 3, 66, 8029, 3484760, 2595985770, 2815099031417, 4230059694039460, 8529853839173455678, 22496718465713456081402, 75951258300080722467845995, 322269241532759484921710401976

Offset: 0

Author

Jason Kimberley, Sep 28 2009

Keywords

• nonn
• hard
• more

Links

• N. J. A. Sloane, Transforms
• Jason Kimberley, Disconnected regular graphs (with girth at least 3)
• Jason Kimberley, Index of sequences counting disconnected k-regular simple graphs with girth at least g
• Eric Weisstein's World of Mathematics, Disconnected Graph
• Eric Weisstein's World of Mathematics, Quintic Graph

Crossrefs

5-regular simple graphs: A006821 (connected), this sequence (disconnected), A165626 (not necessarily connected).

Disconnected regular simple graphs: A068932 (any degree), A068933 (triangular array), specified degree k: A165652 (k=2), A165653 (k=3), A033483 (k=4), this sequence (k=5), A165656 (k=6), A165877 (k=7), A165878 (k=8), A185293 (k=9), A185203 (k=10), A185213 (k=11).

Formula

a = A165626 - A006821 = Euler_transformation(A006821) - A006821.

a(n)=A068933(2n,5).

Extensions

Terms a(13)-a(17), due to the extension of A006821 by Andrew Howroyd, from Jason Kimberley, Mar 12 2020