A338604 -id:A338604 - cp's OEIS frontend

A123545 Triangle read by rows: T(n,k) = number of unlabeled connected graphs on n nodes with degree >= 3 at each node (n >= 1, 0 <= k <= n(n-1)/2).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 4, 5, 4, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 18, 30, 34, 29, 17, 9, 5, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 35, 136, 309, 465, 505, 438, 310, 188, 103, 52, 23

Offset: 1

N. J. A. Sloane, Nov 13 2006

			Triangle begins:
n = 1
k = 0 : 0
************************ TOTAL (n = 1) = 0
n = 2
k = 0 : 0
k = 1 : 0
************************ TOTAL (n = 2) = 0
n = 3
k = 0 : 0
k = 1 : 0
k = 2 : 0
k = 3 : 0
************************ TOTAL (n = 3) = 0
n = 4
k = 0 : 0
k = 1 : 0
k = 2 : 0
k = 3 : 0
k = 4 : 0
k = 5 : 0
k = 6 : 1
************************ TOTAL (n = 4) = 1
n = 5
k = 0 : 0
k = 1 : 0
k = 2 : 0
k = 3 : 0
k = 4 : 0
k = 5 : 0
k = 6 : 0
k = 7 : 0
k = 8 : 1
k = 9 : 1
k = 10 : 1
************************ TOTAL (n = 5) = 3
From _Hugo Pfoertner_, Nov 22 2020: (Start)
Transposed table:
                            Nodes                             Sums
       4  5  6   7    8      9      10      11     12    13 |A338604
  Edges-----------------------------------------------------|-------
   6 | 1  .  .   .    .      .       .       .      .     . |      1
   7 | .  .  .   .    .      .       .       .      .     . |      0
   8 | .  1  .   .    .      .       .       .      .     . |      1
   9 | .  1  2   .    .      .       .       .      .     . |      3
  10 | .  1  4   .    .      .       .       .      .     . |      5
  11 | .  .  5   4    .      .       .       .      .     . |      9
  12 | .  .  4  18    5      .       .       .      .     . |     27
  13 | .  .  2  30   35      .       .       .      .     . |     67
  14 | .  .  1  34  136     27       .       .      .     . |    198
  15 | .  .  1  29  309    288      19       .      .     . |    646
  16 | .  .  .  17  465   1377     357       .      .     . |   2216
  17 | .  .  .   9  505   3978    3478     208      .     . |   8178
  18 | .  .  .   5  438   7956   18653    4958     85     . |  32085
  19 | .  .  .   2  310  11904   65011   50575   4291     . | 132093
  20 | .  .  .   1  188  14134  163812  302854  85421  1958 | 568368
(End)

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.

R. W. Robinson, Rows 1 through 14, flattened

Row sums give A007112. Cf. A123546, A338604.

A338593 Number of unlabeled connected nonplanar graphs with n edges with degree >= 3 at each node.

Original entry on oeis.org

1, 2, 3, 10, 30, 100, 371, 1419, 5764, 24482, 107583, 487647, 2271488, 10847623

Offset: 9

Hugo Pfoertner, Nov 21 2020

First differs from A338583 for n = 13. All unlabeled nonplanar graphs with n <= 12 edges and degree >= 3 at each node are 3-connected. For this reason the illustrations of the graphs are identical up to n = 12. The first differences for n = 13 and n = 14 are shown in the illustrations of A338584.

Hugo Pfoertner, Illustrations of terms a(9) - a(12), from A338583.
Hugo Pfoertner, Illustration of terms a(13) and a(14), showing graphs counted in this sequence, but not in A338583 (illustrations from A338584).
Hugo Pfoertner, Unlabeled nonplanar graphs with vertex degree >=3 for n<=19 edges, list in PARI-readable format.

Cf. A007112, A002840, A123545, A338511, A338583, A338584, A338594, A338604.

\\ It is assumed that the a338593.gp file (from the linked zip archive) has been read before, i.e., \r [path]a338593.gp
for(k=9,#EdgeDataNonplanarDegge3,print1(#EdgeDataNonplanarDegge3[k],", "));
\\ printing of the edge lists of the graphs for n <= 11
print(EdgeDataNonplanarDegge3[9..11])

a(n) = A338604(n) - A338594(n).

A052448 Number of simple unlabeled n-node graphs of edge-connectivity 3.

Original entry on oeis.org

0, 0, 0, 1, 2, 15, 121, 2159, 68715, 3952378, 389968005, 65161587084

Offset: 1

Eric W. Weisstein, May 08 2000

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
T. Hoppe and A. Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014.
Jens M. Schmidt, Combinatorial data.
Eric Weisstein's World of Mathematics, k-Edge Connected Graph.

Column k=3 of A263296.
Cf. other edge-connectivity unlabeled graph sequences A052446, A052447, A241703, A241704, A241705.
Cf. A338511, A338583, A338593, A338594, A338604, A339072.

a(8), a(9), a(10) from the Encyclopedia of Finite Graphs by Travis Hoppe and Anna Petrone, Apr 22 2014
a(11) by Jens M. Schmidt, Feb 18 2019
a(12) from Jens M. Schmidt's web page, Jan 10 2021

A338594 Number of unlabeled connected planar graphs with n edges with degree >= 3 at each node.

Original entry on oeis.org

1, 0, 1, 2, 3, 6, 17, 37, 98, 275, 797, 2414, 7613, 24510, 80721, 270018, 915034

Offset: 6

Hugo Pfoertner, Nov 21 2020

			a(6) = 1: the 3-connected edge graph of the tetrahedron;
a(7) = 0: no connected planar graph with degree >=3 at each node exists;
a(8) = 1: the 3-connected 5-wheel graph, edge graph of 4-sided pyramid;
a(9)-a(11): see linked illustrations.

Hugo Pfoertner, Illustrations of terms a(9) - a(11).

Cf. A007112, A002840, A123545, A338511, A338583, A338584, A338593, A338604.

a(n) = A338604(n) - A338593(n).

A338583 Number of unlabeled 3-connected nonplanar graphs with n edges.

Original entry on oeis.org

1, 2, 3, 10, 29, 94, 343, 1291, 5206, 22061, 96908, 439837, 2053916, 9841412, 48319944, 242857491, 1248629027, 6563581656, 35258560001, 193463945790

Offset: 9

Hugo Pfoertner, Nov 21 2020

Hugo Pfoertner, Illustrations of terms a(9) - a(12).

Cf. A002840, A006290, A337517, A338197, A338511, A338573, A338584, A338593, A338594, A338604.

a(n) = A338511(n) - A002840(n).

a(n) <= A338593(n). The difference A338584(n) = A338593(n)-a(n) are the counts of nonplanar connected graphs with minimum degree 3 at each node that are not 3-connected.

A338584 Number of unlabeled nonplanar connected graphs with n edges with minimum degree 3 at each node that are not 3-connected.

Original entry on oeis.org

1, 6, 28, 128, 558, 2421, 10675, 47810, 217572, 1006211

Offset: 13

Hugo Pfoertner, Nov 21 2020

Hugo Pfoertner, Illustration of terms a(13) and a(14).

Cf. A006290, A007112, A123545, A338583, A338593, A338594, A338604.

a(n) = A338593(n) - A338583(n).

cp's OEIS Frontend

A123545 Triangle read by rows: T(n,k) = number of unlabeled connected graphs on n nodes with degree >= 3 at each node (n >= 1, 0 <= k <= n(n-1)/2).

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A338593 Number of unlabeled connected nonplanar graphs with n edges with degree >= 3 at each node.

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A052448 Number of simple unlabeled n-node graphs of edge-connectivity 3.

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A338594 Number of unlabeled connected planar graphs with n edges with degree >= 3 at each node.

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A338583 Number of unlabeled 3-connected nonplanar graphs with n edges.

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A338584 Number of unlabeled nonplanar connected graphs with n edges with minimum degree 3 at each node that are not 3-connected.

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