A004109 - OEIS

A004109

Number of connected trivalent (or cubic) labeled graphs with 2n nodes.
(Formerly M5345)

1, 0, 1, 70, 19320, 11166120, 11543439600, 19491385914000, 50233275604512000, 187663723374359232000, 975937986889287117696000, 6838461558851342749449120000, 62856853767402275979616458240000, 741099150663748252073618880960000000, 10997077750618335243742188527076864000000

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,4

REFERENCES

R. C. Read, Some Enumeration Problems in Graph Theory. Ph.D. Dissertation, Department of Mathematics, Univ. London, 1958.

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.

R. W. Robinson, Computer print-out, no date. Gives first 29 terms.

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

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..100 (terms 1..29 from R. W. Robinson)

Élie de Panafieu, Asymptotic expansion of regular and connected regular graphs, arXiv:2408.12459 [math.CO], 2024. See p. 13.

R. C. Read, Letter to N. J. A. Sloane, Feb 04 1971 (gives initial terms of this sequence)

R. W. Robinson, Cubic labeled graphs, computer print-out, n.d.

FORMULA

Conjecture: a(n) ~ 2^(n + 1/2) * 3^n * n^(3*n) / exp(3*n+2). - Vaclav Kotesovec, Feb 17 2024

EXAMPLE

From R. J. Mathar, Oct 18 2018: (Start)

For n=3, 2*n=6, the A002851(n)=2 graphs have multiplicities of 10 and 60 (sum 70).

For n=4, 2*n=8, the A002851(n)=5 graphs have multiplicities of 3360, 840, 2520, 10080 and 2520, (sum 19320). (The orders of the five Aut-groups are 8!/3360 =12, 8!/840=48, 8!/2520 =16, 8!/10080=4 and 8!/2520=16, i.e., all larger than 1 as indicated in A204328). (End)

CROSSREFS

See A002829 for not-necessarily-connected graphs, A002851 for connected unlabeled cases.

Cf. A324163.

Sequence in context: A103157 A364305 A007099 * A002829 A177637 A145410

Adjacent sequences: A004106 A004107 A004108 * A004110 A004111 A004112

KEYWORD

nonn,nice

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(0)=1 prepended by Andrew Howroyd, Sep 02 2019

STATUS

approved