A338594 -id:A338594 - cp's OEIS frontend

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

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

A338604 Number of unlabeled connected graphs with n edges with degree >= 3 at each node.

Original entry on oeis.org

1, 0, 1, 3, 5, 9, 27, 67, 198, 646, 2216, 8178, 32095, 132093, 568368, 2541506, 11762657, 56183633, 276288402, 1396172601, 7238931364

Offset: 6

Hugo Pfoertner, Nov 21 2020

			a(10)=5:
There are 5 graphs with 10 edges and degree >=3 at all nodes (see table in A123545):
The complete graph on 5 nodes, given by the edge list
[[1,2],[1,3],[1,4],[1,5],[2,3],[2,4],[2,5],[3,4],[3,5],[4,5]],
and 4 graphs on 6 nodes:
  [[1,3],[1,5],[1,6],[2,4],[2,5],[2,6],[3,5],[3,6],[4,5],[4,6]],
  [[1,4],[1,5],[1,6],[2,4],[2,5],[2,6],[3,4],[3,5],[3,6],[4,6]],
  [[1,3],[1,4],[1,6],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6],[5,6]],
  [[1,3],[1,4],[1,5],[1,6],[2,4],[2,5],[2,6],[3,5],[3,6],[4,6]].
The first one has degree 3 or 4 at all nodes, but becomes disconnected by removing nodes 5 and 6 and their incident edges. It is therefore not 3-connected.
    .--5--.
   /  / \  \
  1--3   4--2
   \  \ /  /
    .--6--.
.
The complete graph on 5 nodes and the last 3 graphs with 6 nodes are all 3-connected. Thus A338511(10)=4, and by inclusion of the graph shown above a(10)=5.

Cf. A007112, A123545, A338511, A338593, A338594.

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

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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A338604 Number of unlabeled connected 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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