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A005638 Number of unlabeled trivalent (or cubic) graphs with 2n nodes.
(Formerly M1656)
1, 0, 1, 2, 6, 21, 94, 540, 4207, 42110, 516344, 7373924, 118573592, 2103205738, 40634185402, 847871397424, 18987149095005, 454032821688754, 11544329612485981, 310964453836198311, 8845303172513781271 (list; graph; refs; listen; history; text; internal format)



Because the triangle A051031 is symmetric, a(n) is also the number of (2n-4)-regular graphs on 2n vertices.


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

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


Table of n, a(n) for n=0..20.

G. Brinkmann, Fast generation of cubic graphs, Journal of Graph Theory, 23(2):139-149, 1996.

Jason Kimberley, Not-necessarily connected regular graphs

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

R. W. Robinson, Cubic graphs (notes)

Robinson, R. W.; Wormald, N. C., Numbers of cubic graphs, J. Graph Theory 7 (1983), no. 4, 463-467.

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, Cubic Graph


a(n) = A002851(n) + A165653(n).

This sequence is the Euler transformation of A002851.


Cf. A000421.

Row sums of A275744.

3-regular simple graphs: A002851 (connected), A165653 (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), this sequence (k=3), A033301 (k=4), A165626 (k=5), A165627 (k=6), A165628 (k=7), A180260 (k=8).

Not necessarily connected 3-regular simple graphs with girth *at least* g: this sequence (g=3), A185334 (g=4), A185335 (g=5), A185336 (g=6).

Not necessarily connected 3-regular simple graphs with girth *exactly* g: A185133 (g=3), A185134 (g=4), A185135 (g=5), A185136 (g=6).

Sequence in context: A214087 A183950 A001928 * A249395 A008988 A061232

Adjacent sequences:  A005635 A005636 A005637 * A005639 A005640 A005641




N. J. A. Sloane.


More terms from R. C. Read (rcread(AT)math.uwaterloo.ca).

Comment, formulas, and (most) crossrefs by Jason Kimberley, 2009 and 2012



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