OFFSET
1,2
COMMENTS
a(n) is also the number of isomorphism classes of connected 3-regular 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. 63-105 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
Jan-Peter Börnsen, Anton E. M. van de Ven, Tangent Developable Orbit Space of an Octupole, arXiv:1807.04817 [hep-th], 2018.
G. Brinkmann, N. Van Cleemput, T. Pisanski, Generation of various classes of trivalent graphs, Theoretical Computer Science 502, 2013, pp.16-29.
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
KEYWORD
nonn,hard,more
AUTHOR
EXTENSIONS
More terms from Brendan McKay, Apr 15 2007
a(13)-a(20) from Andrew Howroyd, Mar 19 2020
STATUS
approved