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

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

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

• 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.

Crossrefs

Column k=3 of A333397.

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

Formula

Inverse Euler transform of A129427.

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