A123542 -id:A123542 - cp's OEIS frontend

A339072 Triangle read by rows: T(n,k) is the number of unlabeled simple 3-connected graphs with n nodes and k edges (n >= 4, ceiling(3n/2) <= k <= n(n-1)/2).

1, 1, 1, 1, 2, 3, 4, 4, 2, 1, 1, 3, 14, 25, 31, 28, 17, 9, 5, 2, 1, 1, 4, 24, 101, 254, 413, 475, 426, 306, 187, 103, 52, 23, 11, 5, 2, 1, 1, 19, 204, 1068, 3348, 7152, 11199, 13683, 13604, 11374, 8203, 5216, 2963, 1536, 737, 333, 144, 62, 25, 11, 5, 2, 1, 1

Offset: 4

Andrew Howroyd, Nov 24 2020

			Triangle begins:
===========================================================
n/k | 6  7  8   9  10 11  12  13  14  15  16 17 18 19 20 21
----+------------------------------------------------------
  4 | 1;
  5 |       1,  1,  1;
  6 |           2,  3, 4,  4,  2,  1,  1;
  7 |                  3, 14, 25, 31, 28, 17, 9, 5, 2, 1, 1;
  8 |                      4, 24 ...
  ...

Andrew Howroyd, Table of n, a(n) for n = 4..732 (rows n=4..18, extracted from Robinson's tables)
R. W. Robinson, Tables of 2-Connected and 3-Connected Graphs by Nodes and Edges, Table VI, pages 19-27.

Row sums are A006290.
Column sums are A338511.
Cf. A054924, A123542, A339071.

A005644 Number of labeled 3-connected graphs with n nodes.

Original entry on oeis.org

1, 26, 1768, 225096, 51725352, 21132802544, 15463799747936, 20604021770403328, 50928019401158515328, 237644423948928994197504, 2125373296900166452199861760, 36884133903194627014531723872256

Offset: 4

N. J. A. Sloane

nonn

Miklos Bona, editor, Handbook of Enumerative Combinatorics, CRC Press, 2015, p. 403.
R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1976.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

R. W. Robinson, Table of n, a(n) for n = 4..25
T. R. S. Walsh, Counting labeled three-connected and homeomorphically irreducible two-connected graphs, J. Combin. Theory Ser. B 32 (1982), no. 1, 1-11.

Row sums of A123542.

Corrected and extended by N. J. A. Sloane, Nov 13 2006

A338414 Number of labeled 3-connected graphs with n edges.

Original entry on oeis.org

1, 0, 15, 80, 493, 5730, 45790, 501690, 5747805, 66738169, 884847355, 12032825028, 174686734180, 2698980641742, 43470161714616, 739558796434277, 13161203468888236, 244555222834161480

Offset: 6

Andrew Howroyd, Nov 07 2020

The initial terms of this sequence were computed from A123542.

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

Cf. A005644, A007100, A123542, A322139, A338511.

cp's OEIS Frontend

A339072 Triangle read by rows: T(n,k) is the number of unlabeled simple 3-connected graphs with n nodes and k edges (n >= 4, ceiling(3n/2) <= k <= n(n-1)/2).

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A005644 Number of labeled 3-connected graphs with n nodes.

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A338414 Number of labeled 3-connected graphs with n edges.

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cp's OEIS Frontend

A339072 Triangle read by rows: T(n,k) is the number of unlabeled simple 3-connected graphs with n nodes and k edges (n >= 4, ceiling(3*n/2) <= k <= n*(n-1)/2).

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A005644 Number of labeled 3-connected graphs with n nodes.

Views

Author

Keywords

References

Links

Crossrefs

Extensions

A338414 Number of labeled 3-connected graphs with n edges.

Views

Author

Keywords

Comments

Crossrefs

A339072 Triangle read by rows: T(n,k) is the number of unlabeled simple 3-connected graphs with n nodes and k edges (n >= 4, ceiling(3n/2) <= k <= n(n-1)/2).