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A033301 Number of 4-valent (or quartic) graphs with n nodes. 18
1, 0, 0, 0, 0, 1, 1, 2, 6, 16, 60, 266, 1547, 10786, 88193, 805579, 8037796, 86223660, 985883873, 11946592242, 152808993767, 2056701139136, 28566369866514 (list; graph; refs; listen; history; text; internal format)



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]


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


Table of n, a(n) for n=0..22.

M. Meringer, Tables of Regular Graphs

M. Meringer, Erzeugung Regulaerer 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


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


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).

Sequence in context: A006820 A131385 A027742 * A197102 A093113 A150030

Adjacent sequences:  A033298 A033299 A033300 * A033302 A033303 A033304




R. C. Read (rcread(AT)math.uwaterloo.ca)


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

a(17)-a(19), a(21) from Jason Kimberley, Sep 2009 and Oct 2011

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



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Last modified January 16 13:32 EST 2019. Contains 319193 sequences. (Running on oeis4.)