The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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)



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).


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

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.


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)


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

Cf. A324163.

Sequence in context: A007100 A103157 A007099 * A002829 A177637 A145410

Adjacent sequences:  A004106 A004107 A004108 * A004110 A004111 A004112




N. J. A. Sloane


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



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 16 05:26 EDT 2021. Contains 343030 sequences. (Running on oeis4.)