A242792 -id:A242792 - cp's OEIS frontend

A243249 Number of unlabeled, connected graphs on n vertices with at least one subgraph isomorphic to a bowtie graph.

Original entry on oeis.org

0, 0, 0, 0, 6, 52, 580, 9348, 246244, 11542460

Offset: 1

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, Bowtie or Butterfly Graph

a(n) = A001349(n) - A242792(n).

A243545 Number of simple connected graphs with n nodes that are Hamiltonian and have no subgraph isomorphic to the bowtie graph.

Original entry on oeis.org

1, 0, 1, 3, 3, 14, 50, 390, 3627, 52858, 1045177

Offset: 1

Travis Hoppe and Anna Petrone, Jun 06 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.
F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version a1db88e

Cf. A242792 (bowtie free graphs), A003216 (Hamiltonian graphs).

a(11) added using tinygraph by Falk Hüffner, Aug 15 2017

A243546 Number of simple connected graphs with n nodes that are distance regular and have no subgraph isomorphic to the bowtie graph.

Original entry on oeis.org

1, 1, 1, 2, 1, 2, 1, 3, 1, 4

Offset: 1

Travis Hoppe and Anna Petrone, Jun 06 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, 2014

Cf. A242792 (bowtie free graphs), A241814 (distance regular graphs).

A243547 Number of simple connected graphs with n nodes that are Eulerian and have no subgraph isomorphic to the bowtie graph.

Original entry on oeis.org

1, 0, 1, 1, 2, 4, 8, 35, 115, 629

Offset: 1

Travis Hoppe and Anna Petrone, Jun 06 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, 2014

Cf. A242792 (bowtie free graphs), A003049 (Eulerian graphs).

A243548 Number of simple connected graphs with n nodes that are integral and have no subgraph isomorphic to the bowtie graph.

Original entry on oeis.org

1, 1, 1, 2, 2, 4, 1, 8, 1, 19

Offset: 1

Travis Hoppe and Anna Petrone, Jun 06 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, 2014

Cf. A242792 (bowtie free graphs), A064731 (integral graphs).

A243549 Number of simple connected graphs with n nodes that are non-integral and have no subgraph isomorphic to the bowtie graph.

Original entry on oeis.org

0, 0, 1, 4, 13, 56, 272, 1761, 14835, 174092

Offset: 1

Travis Hoppe and Anna Petrone, Jun 06 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.

Cf. A242792 (bowtie-free graphs), A241842 (non-integral graphs).

A243550 Number of simple connected graphs with n nodes that are planar and have no subgraph isomorphic to the bowtie graph.

Original entry on oeis.org

1, 1, 2, 6, 15, 58, 255, 1510, 10766, 94109, 945773, 10577294

Offset: 1

Travis Hoppe and Anna Petrone, Jun 06 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, 2014
F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 9766535.

Cf. A242792 (bowtie free graphs), A003094 (planar graphs).

a(11)-a(12) added using tinygraph by Falk Hüffner, May 09 2019

A243551 Number of simple connected graphs with n nodes that have no subgraph isomorphic to the bowtie graph or K_4.

Original entry on oeis.org

1, 1, 2, 5, 14, 56, 256, 1656, 13952, 163878, 2646642, 59088801

Offset: 1

Travis Hoppe and Anna Petrone, Jun 06 2014

K_4 is the complete graph on four vertices.

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, 2014
F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 29e68fa.

Cf. A242792 (bowtie free graphs), A079574 (K_4 free graphs).

a(11)-a(12) added using tinygraph by Falk Hüffner, Sep 23 2020

A243552 Number of simple connected graphs with n nodes that have no subgraph isomorphic to the bowtie graph or bull graph.

Original entry on oeis.org

1, 1, 2, 6, 8, 25, 77, 333, 1668, 11355

Offset: 1

Travis Hoppe and Anna Petrone, Jun 06 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, 2014

Cf. A242792 (no bowtie subgraphs), A244427 (no bull subgraphs).

A243567 Number of simple connected graphs with n nodes that are have no subgraph isomorphic to diamond graph or the bowtie graph.

Original entry on oeis.org

1, 1, 2, 4, 10, 36, 141, 784, 5626, 56249, 774266, 14750595

Offset: 1

Travis Hoppe and Anna Petrone, Jun 06 2014

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 29e68fa.

Cf. A242790 (diamond free graphs), A242792 (bowtie free graphs).

a(11)-a(12) added using tinygraph by Falk Hüffner, Sep 23 2020

cp's OEIS Frontend

A243249 Number of unlabeled, connected graphs on n vertices with at least one subgraph isomorphic to a bowtie graph.

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A243545 Number of simple connected graphs with n nodes that are Hamiltonian and have no subgraph isomorphic to the bowtie graph.

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A243546 Number of simple connected graphs with n nodes that are distance regular and have no subgraph isomorphic to the bowtie graph.

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A243547 Number of simple connected graphs with n nodes that are Eulerian and have no subgraph isomorphic to the bowtie graph.

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A243548 Number of simple connected graphs with n nodes that are integral and have no subgraph isomorphic to the bowtie graph.

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A243549 Number of simple connected graphs with n nodes that are non-integral and have no subgraph isomorphic to the bowtie graph.

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A243550 Number of simple connected graphs with n nodes that are planar and have no subgraph isomorphic to the bowtie graph.

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A243551 Number of simple connected graphs with n nodes that have no subgraph isomorphic to the bowtie graph or K_4.

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Extensions

A243552 Number of simple connected graphs with n nodes that have no subgraph isomorphic to the bowtie graph or bull graph.

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A243567 Number of simple connected graphs with n nodes that are have no subgraph isomorphic to diamond graph or the bowtie graph.

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