cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A366315 Number of Harris graphs with n vertices. Harris graphs are 1-tough, Eulerian graphs that are non-Hamiltonian.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 3, 26, 340, 7297, 233608
Offset: 1

Views

Author

Shubhra Mishra, Oct 06 2023

Keywords

Comments

There are no Harris graphs with 6 or fewer vertices.

Examples

			a(7)=1 because the only Harris graph of 7 vertices (0..6) has edges {(0,1), (0,2), (0,3), (0,4), (1,2), (1,3), (1,5), (2,3), (2,6), (3,4), (3,5), (3,6)}. - _Sean A. Irvine_, Oct 18 2023

Links

Crossrefs

Cf. A007031.

Extensions

a(11)-a(12) from Sean A. Irvine, Oct 18 2023

A342971 Non-1-tough simplicial polyhedra with n nodes.

Original entry on oeis.org

1, 2, 29, 233, 2297, 21192, 195862
Offset: 11

Views

Author

William P. Orrick, Apr 01 2021

Keywords

Comments

A graph is 1-tough if there is no set of k vertices whose deletion splits the graph into more than k components.
If a graph is not 1-tough then it is not Hamiltonian.

Crossrefs

Cf. A000109, A115340, A007030, A007031.

Formula

a(n) = A007030(n) - A007031(n).

A366755 Number of 1-tough unlabeled graphs on n vertices.

Original entry on oeis.org

1, 1, 1, 3, 8, 48, 387, 6240, 178176
Offset: 1

Views

Author

Pontus von Brömssen, Oct 20 2023

Keywords

Examples

			For n = 5, all but two of the A002218(5) = 10 2-connected graphs are 1-tough, so a(5) = 8. The exceptions are the complete bipartite graph K_{2,3} and the complete tripartite graph K_{1,1,3}. To see that these graphs are not 1-tough, note that, in both cases, two vertices can be removed resulting in a graph with three components (isolated vertices).

Links

Crossrefs

Cf. A002218, A007031, A366315, A366756.

Formula

a(n) <= A002218(n) for n >= 2 because all 1-tough graphs (except the 1-node graph) are 2-connected.
Showing 1-3 of 3 results.

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