A002880 -id:A002880 - cp's OEIS frontend

A113205 Same as A002880, but with orientation-reversing isomorphisms forbidden.

1, 0, 1, 1, 3, 2, 12, 16, 59, 133, 445, 1248, 4162, 13014, 43474, 143304, 484444, 1639388, 5617205, 19332596, 67048051, 233691112, 819121608, 2884443024, 10204104900, 36247138920, 129264732757, 462661038926, 1661637913984

Offset: 6

N. J. A. Sloane, Jan 07 2006

nonn

G. Brinkmann, S. Greenberg, C. Greenhill, B. D. McKay, R. Thomas, and P. Wollan, Generation of simple quadrangulations of the sphere, Discr. Math., 305 (2005), 33-54.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
CombOS - Combinatorial Object Server, generate planar graphs

Cf. A113201, A078666, A007022, A002880, A113202, A113203, A113204.

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

Original entry on oeis.org

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

A113201 Number of isomorphism classes of simple quadrangulations of the sphere having n vertices and n-2 faces, with orientation-reversing isomorphisms permitted.

Original entry on oeis.org

1, 1, 2, 3, 9, 18, 62, 198, 803, 3378, 15882, 77185, 393075, 2049974, 10938182, 59312272, 326258544, 1815910231, 10213424233, 57974895671, 331820721234, 1913429250439, 11109119321058, 64901418126997

Offset: 4

N. J. A. Sloane, Jan 07 2006

nonn

G. Brinkmann, S. Greenberg, C. Greenhill, B. D. McKay, R. Thomas, and P. Wollan, Generation of simple quadrangulations of the sphere, Discr. Math., 305 (2005), 33-54.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
J. Cantarella, H. Chapman, M. Mastin, Knot Probabilities in Random Diagrams, arXiv preprint arXiv:1512.05749 [math.GT], 2015. See Tables 1.
CombOS - Combinatorial Object Server, generate planar graphs
Paul Jungeblut, Edge Guarding Plane Graphs, Master Thesis, Karlsruhe Institute of Technology (Germany, 2019).
Sage, Common Graphs

Cf. A078666, A007022, A002880.

A113204 Same as A007022, but with orientation-reversing isomorphisms forbidden.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 0, 1, 1, 4, 3, 15, 25, 92, 234, 803, 2469, 8512, 28290, 98148, 338673, 1188338, 4180854, 14840031, 52904562, 189724510, 683384218, 2472961423, 8984888982, 32772085447, 119963084542, 440623586740, 1623555117611

Offset: 1

N. J. A. Sloane, Jan 07 2006

nonn

G. Brinkmann, S. Greenberg, C. Greenhill, B. D. McKay, R. Thomas, and P. Wollan, Generation of simple quadrangulations of the sphere, Discr. Math., 305 (2005), 33-54. doi:10.1016/j.disc.2005.10.005
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
CombOS - Combinatorial Object Server, generate planar graphs

Cf. A113201, A078666, A007022, A002880, A113202, A113205.

a(29) corrected by Brendan McKay, Jun 22 2006
Leading zeros prepended by Max Alekseyev, Sep 13 2016
Offset corrected by Andrey Zabolotskiy, Feb 09 2018

A113202 Number of isomorphism classes of simple quadrangulations of the sphere having n vertices and n-2 faces, with orientation-reversing isomorphisms forbidden.

Original entry on oeis.org

1, 1, 2, 3, 10, 21, 83, 298, 1339, 6049, 29765, 148842, 770267, 4054539, 21743705, 118237471, 651370528, 3628421181, 20416662314, 115919209155, 663548898942, 3826577783917, 22217382001865, 129800215435088

Offset: 4

N. J. A. Sloane, Jan 07 2006

nonn

G. Brinkmann, S. Greenberg, C. Greenhill, B. D. McKay, R. Thomas, and P. Wollan, Generation of simple quadrangulations of the sphere, Discr. Math., 305 (2005), 33-54.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
CombOS - Combinatorial Object Server, generate planar graphs

Cf. A113201, A078666, A007022, A002880, A113203, A113204, A113205.

A113203 Number of isomorphism classes of simple quadrangulations of the sphere having n vertices and n-2 faces, minimal degree 3, with orientation-reversing isomorphisms forbidden.

Original entry on oeis.org

1, 0, 1, 1, 4, 3, 16, 26, 99, 256, 895, 2789, 9740, 32799, 115024, 401180, 1421170, 5046539, 18066772, 64940825, 234712099, 851801048, 3104690139, 11358900851, 41710948878, 153684688127, 568079430741, 2106188450292

Offset: 8

N. J. A. Sloane, Jan 07 2006

nonn

G. Brinkmann, S. Greenberg, C. Greenhill, B. D. McKay, R. Thomas, and P. Wollan, Generation of simple quadrangulations of the sphere, Discr. Math., 305 (2005), 33-54.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph [Cached copy, pdf file only, no active links, with permission]
CombOS - Combinatorial Object Server, generate planar graphs

Cf. A113201, A078666, A007022, A002880, A113202, A113204, A113205.

cp's OEIS Frontend

A113205 Same as A002880, but with orientation-reversing isomorphisms forbidden.

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

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A113201 Number of isomorphism classes of simple quadrangulations of the sphere having n vertices and n-2 faces, with orientation-reversing isomorphisms permitted.

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Author

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Links

Crossrefs

A113204 Same as A007022, but with orientation-reversing isomorphisms forbidden.

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Author

Keywords

Links

Crossrefs

Extensions

A113202 Number of isomorphism classes of simple quadrangulations of the sphere having n vertices and n-2 faces, with orientation-reversing isomorphisms forbidden.

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Author

Keywords

Links

Crossrefs

A113203 Number of isomorphism classes of simple quadrangulations of the sphere having n vertices and n-2 faces, minimal degree 3, with orientation-reversing isomorphisms forbidden.

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Author

Keywords

Links

Crossrefs