A187928 -id:A187928 - cp's OEIS frontend

A187927 Number of embeddings on the sphere of 2-connected planar graphs, minimum vertex degree 3, with n nodes.

2, 13, 163, 2067, 30953, 486674, 7957459, 133344454, 2280001754, 39648557743, 699731146514, 12511186297320

Offset: 6

Stuart E Anderson, Mar 16 2011

The graphs are exactly 2-connected, not at least 2-connected. The graphs were enumerated using plantri (by B.D. McKay & G. Brinkmann) for the purpose of finding compound perfect squared squares.

Stuart Anderson, Compound Perfect Squared Squares
S. E. Anderson, Compound Perfect Squared Squares of the Order Twenties, 2013.
Gunnar Brinkmann and Brendan McKay, Plantri Guide
Gunnar Brinkmann and Brendan McKay, Guide to using plantri [Cached copy, with permission]

Cf. A034889, A181340, A187928, A000944.

plantri
```
plantri -p -c2 -m3 -x -u -v n  ; or
```

a(15)-a(17) from Lorenz Milla, Oct 08 2013

A378076 Number of embeddings on the sphere of 2-connected homeomorphically irreducible planar graphs with n edges.

Original entry on oeis.org

1, 0, 1, 2, 3, 6, 16, 37, 100, 293, 888, 2822, 9305, 31274, 106972, 370828, 1298058, 4582413, 16289759, 58259600, 209465186

Offset: 6

Andrew Howroyd, Nov 15 2024

Homeomorphically irreducible means each vertex has a degree of at least 3.

Antidiagonal sums of A378075.

Cf. A002840, A006407, A187928.

a(n) = A002840(n) + A187928(n).

a(n) = Sum_{k=4..n-2} A378075(k, n+2-k).

A378077 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of planar graphs with n vertices and k faces having connectivity exactly 2 and minimum vertex degree at least 3, k=6..2n-5.

Original entry on oeis.org

1, 1, 1, 3, 7, 2, 1, 8, 35, 60, 47, 12, 0, 5, 72, 307, 647, 652, 325, 59, 0, 3, 86, 776, 3395, 7647, 9582, 6654, 2442, 368, 0, 0, 45, 1041, 9091, 38876, 94278, 136628, 121204, 64232, 18916, 2363, 0, 0, 18, 827, 14407, 111076, 468211, 1192511, 1937266, 2049784, 1409199, 607746, 150161, 16253

Offset: 6

Andrew Howroyd, Nov 15 2024

The graphs are 2-connected, but not 3-connected. Graphs with minimum degree at least 3 are also called homeomorphically irreducible.

The number of edges is n + k - 2.

			Triangle begins:
  n\k| 6  7   8     9    10     11     12      13      14     15     16    17
-----+------------------------------------------------------------------------
   6 | 1, 1;
   7 | 1, 3,  7,    2;
   8 | 1, 8, 35,   60,   47,    12;
   9 | 0, 5, 72,  307,  647,   652,   325,     59;
  10 | 0, 3, 86,  776, 3395,  7647,  9582,   6654,   2442,   368;
  11 | 0, 0, 45, 1041, 9091, 38876, 94278, 136628, 121204, 64232, 18916, 2363;
  ...

Andrew Howroyd, Table of n, a(n) for n = 6..95 (rows 6..14)

Rows sums are A187927.
Antidiagonals sums give A187928.
Cf. A378075.

T(n,k) = A212438(n,k) - A378075(n,k).

cp's OEIS Frontend

A187927 Number of embeddings on the sphere of 2-connected planar graphs, minimum vertex degree 3, with n nodes.

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A378076 Number of embeddings on the sphere of 2-connected homeomorphically irreducible planar graphs with n edges.

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A378077 Triangle read by rows: T(n,k) is the number of embeddings on the sphere of planar graphs with n vertices and k faces having connectivity exactly 2 and minimum vertex degree at least 3, k=6..2n-5.

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