A033301 Number of 4-valent (or quartic) graphs with n nodes.

1, 0, 0, 0, 0, 1, 1, 2, 6, 16, 60, 266, 1547, 10786, 88193, 805579, 8037796, 86223660, 985883873, 11946592242, 152808993767, 2056701139136, 29051369533596, 429669276147047, 6640178380127244, 107026751932268789, 1796103830404560857, 31334029441145918974, 567437704731717802783

Offset: 0

Author

Ronald C. Read

Keywords

• nonn
• nice
• hard

Comments

Because the triangle A051031 is symmetric, a(n) is also the number of (n-5)-regular graphs on n vertices. - Jason Kimberley, Sep 22 2009

References

• R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.

Links

• M. Meringer, Tables of Regular Graphs
• M. Meringer, Erzeugung Regulärer Graphen, Diploma thesis, University of Bayreuth, January 1996. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010]
• N. J. A. Sloane, Transforms
• Peter Steinbach, Field Guide to Simple Graphs, Volume 1, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
• Eric Weisstein's World of Mathematics, Quartic Graph

Crossrefs

4-regular simple graphs: A006820 (connected), A033483 (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), A165627 (k=6), A165628 (k=7).

Programs

Mathematica

A006820 = Cases[Import["https://oeis.org/A006820/b006820.txt", "Table"], {, }][[All, 2]];
(* EulerTransform is defined in A005195 *)
EulerTransform[Rest @ A006820] (* Jean-François Alcover, Nov 26 2019, updated Mar 17 2020 *)

Formula

Euler transform of A006820. - Martin Fuller, Dec 04 2006

Extensions

a(16) from Axel Kohnert (kohnert(AT)uni-bayreuth.de), Jul 24 2003

a(17)-a(19) from Jason Kimberley, Sep 12 2009

a(20)-a(21) from Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010

a(22) from Jason Kimberley, Oct 15 2011

a(22) corrected and a(23)-a(28) from Andrew Howroyd, Mar 08 2020