A079574 -id:A079574 - cp's OEIS frontend

A242790 Number of connected diamond-free graphs on n nodes.

1, 1, 2, 4, 11, 39, 165, 967, 7684, 87012, 1410465, 32640019

Offset: 1

Travis Hoppe and Anna Petrone, May 22 2014

An equivalent definition: Number of simple connected graphs with n nodes that are have no subgraph isomorphic to the diamond graph or the complete graph K_4. This is the same because a graph contains a diamond as a subgraph iff it contains a diamond or K_4 as induced subgraph. - Falk Hüffner, Jan 11 2015

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
Falk Hüffner, tinygraph, software for generating integer sequences based on graph properties, version ece94ef.
Eric Weisstein's World of Mathematics, Diamond Graph

Cf. A077269 (connected squarefree graphs).

Cf. also A242790 (diamond free graphs), A079574 (K_4 free graphs).

Entry revised by N. J. A. Sloane, Jan 11 2016

a(11) and a(12) added using tinygraph by Falk Hüffner, Jan 15 2016

A241782 Number of unlabeled, connected graphs on n vertices with no induced subgraph isomorphic to a K_5, where a K_5 is the complete graph on five vertices.

Original entry on oeis.org

1, 1, 2, 6, 20, 107, 802, 10252, 232850, 9905775

Offset: 1

Travis Hoppe and Anna Petrone, Apr 28 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. similar graphs that are K_4 free, A079574.

A243244 Number of unlabeled, connected graphs on n vertices with at least one induced subgraph isomorphic to a K_4, where K_4 is the complete graph on four vertices.

Original entry on oeis.org

0, 0, 0, 1, 4, 30, 317, 5511, 165165, 8932499, 870814993, 153082769374, 48887756906623

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.

a(n) = A001349(n) - A079574(n).

a(11) and a(12) from formula by Falk Hüffner, Jan 14 2016

a(13) from formula by Falk Hüffner, Aug 15 2021

A243276 Number of graphs with n nodes that are Hamiltonian and have no induced subgraph isomorphic to K_4.

Original entry on oeis.org

1, 0, 1, 2, 5, 29, 188, 2481, 52499, 1857651, 104392105

Offset: 1

Travis Hoppe and Anna Petrone, Jun 02 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 4361e42

Cf. A003216 (Hamiltonian graphs), A079574 (connected K_4 free graphs).

a(11) added using tinygraph by Falk Hüffner, Aug 13 2017

A243327 Number of simple connected graphs with n nodes that are K_4 free and not integral.

Original entry on oeis.org

0, 0, 1, 4, 15, 77, 531, 5597, 95900, 2784034

Offset: 1

Travis Hoppe and Anna Petrone, Jun 03 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 [math.CO], 2014.

Cf. A241842 (non-integral graphs), A079574 (K_4-free graphs).

A243333 Number of simple connected graphs with n nodes that are integral and K_4 free.

Original entry on oeis.org

1, 1, 1, 1, 2, 5, 5, 9, 15, 38

Offset: 1

Travis Hoppe and Anna Petrone, Jun 03 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

Cf. A064731 (integral graphs), A079574 (K_4 free graphs).

A243336 Number of simple connected graphs with n nodes that are Eulerian and K_4 free.

Original entry on oeis.org

1, 0, 1, 1, 3, 6, 22, 93, 656, 7484

Offset: 1

Travis Hoppe and Anna Petrone, Jun 03 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

Cf. A003049 (Eulerian graphs), A079574 (K_4 free graphs).

A243337 Number of simple connected graphs with n nodes that are planar and K_4 free.

Original entry on oeis.org

1, 1, 2, 5, 17, 79, 478, 4123, 46666, 648758, 10275896, 177007433

Offset: 1

Travis Hoppe and Anna Petrone, Jun 03 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 [math.CO], 2014.
F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 9766535.

Cf. A003094 (planar graphs), A079574 (K_4 free graphs).

a(11)-a(12) added using tinygraph by Falk Hüffner, May 10 2019

A243339 Number of simple connected graphs with n nodes that are distance regular and K_4 free.

Original entry on oeis.org

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

Offset: 1

Travis Hoppe and Anna Petrone, Jun 03 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

Cf. A241814 (distance regular graphs), A079574 (K_4 free graphs).

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

cp's OEIS Frontend

A242790 Number of connected diamond-free graphs on n nodes.

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A241782 Number of unlabeled, connected graphs on n vertices with no induced subgraph isomorphic to a K_5, where a K_5 is the complete graph on five vertices.

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A243244 Number of unlabeled, connected graphs on n vertices with at least one induced subgraph isomorphic to a K_4, where K_4 is the complete graph on four vertices.

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A243276 Number of graphs with n nodes that are Hamiltonian and have no induced subgraph isomorphic to K_4.

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A243327 Number of simple connected graphs with n nodes that are K_4 free and not integral.

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A243333 Number of simple connected graphs with n nodes that are integral and K_4 free.

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A243336 Number of simple connected graphs with n nodes that are Eulerian and K_4 free.

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A243337 Number of simple connected graphs with n nodes that are planar and K_4 free.

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A243339 Number of simple connected graphs with n nodes that are distance regular and K_4 free.

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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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