

A000421


Number of isomorphism classes of connected 3regular (trivalent, cubic) loopless multigraphs of order 2n.


16



1, 2, 6, 20, 91, 509, 3608, 31856, 340416, 4269971, 61133757, 978098997, 17228295555, 330552900516, 6853905618223, 152626436936272, 3631575281503404, 91928898608055819, 2466448432564961852, 69907637101781318907
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OFFSET

1,2


COMMENTS

a(n) is also the number of isomorphism classes of connected 3regular simple graphs of order 2n with possibly loops.  Nico Van Cleemput, Jun 04 2014
There are no graphs of order 2n+1 satisfying the condition above.  Natan Arie Consigli, Dec 20 2019


REFERENCES

A. T. Balaban, Enumeration of Cyclic Graphs, pp. 63105 of A. T. Balaban, ed., Chemical Applications of Graph Theory, Ac. Press, 1976; see p. 92 [gives incorrect a(6)].
CRC Handbook of Combinatorial Designs, 1996, p. 651 [or: 2006, table 4.40].


LINKS

Table of n, a(n) for n=1..20.
JanPeter BĂ¶rnsen, Anton E. M. van de Ven, Tangent Developable Orbit Space of an Octupole, arXiv:1807.04817 [hepth], 2018.
G. Brinkmann, N. Van Cleemput, T. Pisanski, Generation of various classes of trivalent graphs, Theoretical Computer Science 502, 2013, pp.1629.
R. J. Mathar, Cubic multigraphs A000421
Brendan McKay and others, Nauty Traces


FORMULA

Inverse Euler transform of A129416.  Andrew Howroyd, Mar 19 2020


EXAMPLE

From Natan Arie Consigli, Dec 20 2019: (Start)
a(1) = 1: with two nodes the only viable option is the triple edged path multigraph.
a(2) = 4: with four nodes we have two cases: the tetrahedral graph and the square graph with single and double edges on opposite sides.
(End)


PROG

(nauty/bash) for n in {1..10}; do geng cqD3 $[2*$n]  multig ur3; done # Sean A. Irvine, Sep 24 2015


CROSSREFS

Column k=3 of A328682 (table of kregular nnode multigraphs).
Cf. A129416, A005967 (loops allowed), A129417, A129419, A129421, A129423, A129425, A002851 (no multiedges).
Sequence in context: A027321 A027315 A005965 * A009244 A104985 A210690
Adjacent sequences: A000418 A000419 A000420 * A000422 A000423 A000424


KEYWORD

nonn,hard,more


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from Brendan McKay, Apr 15 2007
a(13)a(20) from Andrew Howroyd, Mar 19 2020


STATUS

approved



