A165627 Number of 6-regular graphs (sextic graphs) on n vertices.

1, 0, 0, 0, 0, 0, 0, 1, 1, 4, 21, 266, 7849, 367860, 21609301, 1470293676, 113314233813, 9799685588961, 945095823831333, 101114579937196179, 11945375659140003692, 1551593789610531820695, 220716215902794066709555, 34259321384370735003091907, 5782740798229835127025560294

Offset: 0

Author

Jason Kimberley, Sep 22 2009

Keywords

• nonn
• hard

Comments

Because the triangle A051031 is symmetric, a(n) is also the number of (n-7)-regular graphs on n vertices.

Links

• Georg Grasegger, Hakan Guler, Bill Jackson, Anthony Nixon, Flexible circuits in the d-dimensional rigidity matroid, arXiv:2003.06648 [math.CO], 2020.
• Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g
• M. Meringer, Tables of Regular Graphs
• M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146.
• N. J. A. Sloane, Transforms
• Eric Weisstein's World of Mathematics, Regular Graph
• Eric Weisstein's World of Mathematics, Sextic Graph

Crossrefs

6-regular simple graphs: A006822 (connected), A165656 (disconnected), this sequence (not necessarily connected).

Regular graphs A005176 (any degree), A051031 (triangular array), chosen degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), A165626 (k=5), this sequence (k=6), A165628 (k=7), A180260 (k=8).

Programs

Mathematica

A006822 = Cases[Import["https://oeis.org/A006822/b006822.txt", "Table"], {, }][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A006822] (* Jean-François Alcover, Dec 04 2019, updated Mar 18 2020 *)

Formula

Euler transformation of A006822.

Extensions

Cross-references edited by Jason Kimberley, Nov 07 2009 and Oct 17 2011

a(17) from Jason Kimberley, Dec 30 2010

a(18)-a(24) from Andrew Howroyd, Mar 07 2020