A128042 -id:A128042 - cp's OEIS frontend

A241715 Erroneous version of column k=7 of A128042.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 1, 6, 20

Offset: 1

Travis Hoppe and Anna Petrone, Apr 27 2014

dead

Number of simple connected graphs with n nodes and girth 7.

See A241711 for additional information.

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.

Cf. other simple connected graphs of girth k, A241711, A241712, A241713, A241714.

A128236 Number of n-node (unlabeled) graphs with girth 3.

Original entry on oeis.org

1, 4, 20, 118, 937, 11936, 272771, 11992996, 1018892793, 165089910412, 50502010570950, 29054155189364119, 31426485955571756316, 64001015703946097640927, 245935864153501211843554826

Offset: 3

Keith Briggs, May 05 2007

nonn

a(n) = A000088(n) - A006785(n).

Cf. A128041, A128042, A128237-A128243.

Corrected and extended by Martin Fuller, May 01 2015

A128243 Number of n-node (unlabeled) connected graphs with girth 6.

Original entry on oeis.org

0, 0, 0, 1, 1, 6, 17, 69, 239, 962, 3864, 17049, 79607, 403758, 2209386, 13138818, 84841130, 595825731

Offset: 3

Keith Briggs, May 05 2007

Cf. A128041, A128042.

Cf. A128236, A128237, A128238, A128239, A128240, A128241, A128242.

geng -ctfq $n | countg -qg6 --ng # Martin Fuller, May 03 2015

Corrected and extended by Martin Fuller, May 01 2015

a(18)-a(20) added by Georg Grasegger, May 02 2023

A128041 Triangle read by columns: number of n-node (unlabeled) graphs with girth k, for n >= 3, k >= 3.

Original entry on oeis.org

1, 4, 1, 20, 3, 1, 118, 15, 2, 1, 937, 59, 8, 2, 1, 11936, 296, 26, 9, 2, 1, 272771, 1604, 101, 28, 8, 2, 1, 11992996, 11303, 396, 107, 25, 9, 2, 1, 1018892793, 102108, 1744, 376, 92, 29, 9, 2, 1, 165089910412, 1250114, 8531, 1457, 321, 113, 30, 10, 2, 1

Offset: 3

Keith Briggs, May 05 2007

			Number of n-node (unlabeled) graphs with girth k, for n >= 3, k >= 3.
.k..|.n=........3........4........5........6........7........8........9........10
---------------------------------------------------------------------------------
.0..|...........0........0........0........0........0........0........0.........0
.1..|...........0........0........0........0........0........0........0.........0
.2..|...........0........0........0........0........0........0........0.........0
.3..|...........1........4.......20......118......937....11936...272771..11992996
.4..|...........0........1........3.......15.......59......296.....1604.....11303
.5..|...........0........0........1........2........8.......26......101.......396
.6..|...........0........0........0........1........2........9.......28.......107
.7..|...........0........0........0........0........1........2........8........25
.8..|...........0........0........0........0........0........1........2.........9
.9..|...........0........0........0........0........0........0........1.........2
10..|...........0........0........0........0........0........0........0.........1

Cf. A128042, A006787, A128236-A128243.

geng $n | countg --ng # Martin Fuller, May 03 2015

Corrected and extended by Martin Fuller, May 01 2015

A128237 Number of n-node (unlabeled) graphs with girth 4.

Original entry on oeis.org

0, 1, 3, 15, 59, 296, 1604, 11303, 102108, 1250114, 20738069, 467523871, 14230096759, 581439661069, 31720637440030

Offset: 3

Keith Briggs, May 05 2007

nonn

Cf. A006785, A006787.

Cf. A128041, A128042, A128236-A128243.

a(n) = A006785(n) - A006787(n).

Corrected and extended by Martin Fuller, May 01 2015

A128240 Number of n-node (unlabeled) connected graphs with girth 3.

Original entry on oeis.org

0, 0, 1, 3, 15, 93, 794, 10850, 259700, 11706739, 1006609723, 164058686415, 50335888444167, 29003487017067011, 31397381129017616776, 63969560112658419275907, 245871831682052901418048916

Offset: 1

Keith Briggs, May 05 2007

nonn

Number of unlabeled, connected graphs on n vertices with at least one induced subgraph isomorphic to a K_3, where K_3 is the complete graph on three vertices (a triangle). - Travis Hoppe and Anna Petrone, Jun 01 2014

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
Eric Weisstein's World of Mathematics, Triangle-Free Graph

a(n) = A001349(n) - A024607(n).

Cf. A128041, A128042, A128236-A128243.

Corrected and extended by Martin Fuller, May 01 2015

Information added by Falk Hüffner, Nov 27 2015

A128241 Number of n-node (unlabeled) connected graphs with girth 4.

Original entry on oeis.org

0, 1, 2, 11, 41, 220, 1243, 9368, 89049, 1135894, 19381407, 445505570, 13741579905, 566739127723, 31124921885829

Offset: 3

Keith Briggs, May 05 2007

Cf. A024607, A126757.

Cf. A128041, A128042, A128236-A128243.

a(n) = A024607(n) - A126757(n). - Martin Fuller, May 01 2015

Corrected and extended by Martin Fuller, May 01 2015

A325455 Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with circumference k, (n >= 3, k >= 3).

Original entry on oeis.org

1, 1, 3, 4, 6, 8, 10, 24, 24, 48, 30, 87, 116, 226, 383, 83, 342, 527, 1283, 2663, 6196, 257, 1324, 2644, 6644, 17613, 55468, 177083

Offset: 3

Andrew Howroyd, Sep 06 2019

Trees are excluded since they do not have any cycle.

			Triangle begins:
    1;
    1,    3;
    4,    6,    8;
   10,   24,   24,   48;
   30,   87,  116,  226,   383;
   83,  342,  527, 1283,  2663,  6196;
  257, 1324, 2644, 6644, 17613, 55468, 177083;
  ...

Eric Weisstein's World of Mathematics, Graph Circumference
Eric Weisstein's World of Mathematics, Hamiltonian Graph

Right diagonal is A003216.
Row sums are A241841.
Cf. A128042, A309524, A325447.

A128238 Number of n-node (unlabeled) graphs with girth 5.

Original entry on oeis.org

0, 0, 1, 2, 8, 26, 101, 396, 1744, 8531, 47803, 308086, 2300756, 19909540, 199365557

Offset: 3

Keith Briggs, May 05 2007

Cf. A128041, A128042, A128236-A128243.

geng -tfq $n | countg -qg5 --ng # Martin Fuller, May 03 2015

Corrected and extended by Martin Fuller, May 01 2015

A128239 Number of n-node (unlabeled) graphs with girth 6.

Original entry on oeis.org

0, 0, 0, 1, 2, 9, 28, 107, 376, 1457, 5733, 24385, 110240, 540400, 2867847

Offset: 3

Keith Briggs, May 05 2007

Cf. A128041, A128042, A128236-A128243.

geng -tfq $n | countg -qg6 --ng # Martin Fuller, May 03 2015

Corrected and extended by Martin Fuller, May 01 2015

cp's OEIS Frontend

A241715 Erroneous version of column k=7 of A128042.

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A128236 Number of n-node (unlabeled) graphs with girth 3.

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A128243 Number of n-node (unlabeled) connected graphs with girth 6.

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A128041 Triangle read by columns: number of n-node (unlabeled) graphs with girth k, for n >= 3, k >= 3.

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A128237 Number of n-node (unlabeled) graphs with girth 4.

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A128240 Number of n-node (unlabeled) connected graphs with girth 3.

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A128241 Number of n-node (unlabeled) connected graphs with girth 4.

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A325455 Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with circumference k, (n >= 3, k >= 3).

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A128238 Number of n-node (unlabeled) graphs with girth 5.

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nauty

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A128239 Number of n-node (unlabeled) graphs with girth 6.

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