A005967 Number of isomorphism classes of connected 3-regular multigraphs of order 2n, loops allowed. (Formerly M1512)

2, 5, 17, 71, 388, 2592, 21096, 204638, 2317172, 30024276, 437469859, 7067109598, 125184509147, 2410455693765, 50101933643655, 1117669367609605, 26629298567576331, 674793598023809924, 18119844622209998036

Offset

1,1

Comments

a(n) is the number of maximal cells in the moduli space of tropical curves of genus n+1; see Melody Chan (2012) reference. a(n) is also the number of maximally degenerate stable nodal algebraic curves of genus n+1, up to isomorphism, by the association of a stable nodal curve to its dual graph. - Harry Richman, Oct 23 2023

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.

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

Links

Table of n, a(n) for n=1..19.

G. Brinkmann, N. Van Cleemput, and T. Pisanski, Generation of various classes of trivalent graphs, Theor. Comput. Sci. 502 (2013) 16-29, Table 1 column LM.

Melody Chan, Combinatorics of the tropical Torelli map, Algebra Number Theory, 6 (2012), 1133-1169.

Melody Chan, Moduli Spaces of Curves: Classical and Tropical, Notices Amer. Math. Soc., 68 (2021), 1700-1713.

R. de Mello Koch and S. Ramgoolam, Strings from Feynman graph counting: Without large N, Phys. Rev. D 85 (2012) 026007 (D7).

R. J. Mathar, Cubic Multigraphs A005967

R. J. Mathar, Feynman diagrams of the QED vacuum polarization, vixra:1901.0148 (2019).

Brendan McKay, nauty software

Wikipedia, Moduli of algebraic curves.

Formula

Inverse Euler transform of A129427.

Crossrefs

Column k=3 of A333397.

Cf. A129427 (Euler transf.), A000421 (no loops), A085549, A129430, A129432, A129434, A129436.

Sequence in context: A005966 A336282 A082282 * A369402 A104859 A108289

Adjacent sequences: A005964 A005965 A005966 * A005968 A005969 A005970

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Checked by Brendan McKay, Apr 15 2007

Using sequence A129427, terms a(12)-a(16) were computed in GAP by Ignat Soroko, Apr 07 2010

a(17)-a(19) added by Andrew Howroyd, Mar 19 2020

Status

approved