A338414 -id:A338414 - cp's OEIS frontend

A338511 Number of unlabeled 3-connected graphs with n edges.

1, 0, 1, 3, 4, 7, 22, 51, 152, 501, 1739, 6548, 26260, 110292, 483545, 2198726, 10327116, 49965520, 248481062, 1267987437, 6630660484, 35492360163, 194283212876

Offset: 6

Andrew Howroyd, Oct 31 2020

The smallest 3-connected graph is the complete graph on 4 vertices which has 6 edges.

Hugo Pfoertner, 3-connected graphs for n<=18 edges, list in PARI-readable format.
R. W. Robinson, Tables of 2-Connected and 3-Connected Graphs by Nodes and Edges, Table VI, pages 19-27.

Column sums of A339072.

Cf. A002880, A006290, A010355, A338414.

\\ It is assumed that the 3cc.gp file (from the linked zip archive) has been read before, i.e., \r [path]3cc.gp
for(k=1,#ThreeConnectedData,print1(#ThreeConnectedData[k],", "));
\\ printing of the graphs for n <= 9
print(ThreeConnectedData[6..9]) \\ Hugo Pfoertner, Dec 11 2020

a(17)-a(25) from Hugo Pfoertner using data from Robinson's tables, Nov 20 2020

a(26)-a(28) from Andrew Howroyd using data from Robinson's tables, Nov 24 2020

A343871 Number of labeled 3-connected planar graphs with n edges.

Original entry on oeis.org

1, 0, 15, 70, 432, 4320, 30855, 294840, 2883240, 28175952, 310690800, 3458941920, 40459730640, 499638948480, 6324655705200, 83653192972800, 1145266802114400, 16145338385736000, 235579813593453000, 3535776409508703360, 54571687068401395200, 866268656574795936000

Offset: 6

Andrew Howroyd, May 05 2021

nonn

Andrew Howroyd, Table of n, a(n) for n = 6..200
M. Bodirsky, C. Groepl and M. Kang, Generating Labeled Planar Graphs Uniformly At Random, Theoretical Computer Science, Volume 379, Issue 3, 15 June 2007, pp. 377-386.

Cf. A000287, A002840 (unlabeled case), A096330, A290326, A291841, A338414.

Q(n,k) = { \\ c-nets with n-edges, k-vertices (see A290326)
  if (k < 2+(n+2)\3 || k > 2*n\3, return(0));
  sum(i=2, k, sum(j=k, n, (-1)^((i+j+1-k)%2)*binomial(i+j-k,i)*i*(i-1)/2*
  (binomial(2*n-2*k+2,k-i)*binomial(2*k-2, n-j) -
  4*binomial(2*n-2*k+1, k-i-1)*binomial(2*k-3, n-j-1))));
};
a(n)={sum(k=2+(n+2)\3, 2*n\3, k!*Q(n,k))/(4*n)} \\ Andrew Howroyd, May 05 2021

a(n) = Sum_{k=2+floor((n+2)/3)..floor(2*n/3)} k!*A290326(n-k+1, k-1)/(4*n).

cp's OEIS Frontend

A338511 Number of unlabeled 3-connected graphs with n edges.

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