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.

A384639 Number of equivalence classes (up to graph homeomorphism) of finite graphs that have an embedding in an orientable surface of genus n which minimally separates the surface (that is, no proper subset of the embedding separates the genus n surface).

Original entry on oeis.org

1, 5, 26, 217, 3555, 118993
Offset: 0

Views

Author

J. J. P. Veerman, Aug 13 2025

Keywords

Examples

			For genus 0: only the circle.
For genus 1: 1 circle, 2 circles, bouquet of 2 circles, bouquet of 3 circles, 4-fold multi-edge.

References

  • C. N. Aagaard and J. J. P. Veerman, Classification of Minimal Separating Sets of Low Genus Surfaces, Topology and its Applications, Accepted, 2025.
  • J. Bernhard and J. J. P. Veerman, The Topology of Surface Mediatrices, Topology and its Applications, 154, 54-68, 2007.

Crossrefs

Cf. A387066, A387067, A387068.

A387066 Number of equivalence classes (up to graph homeomorphism) of finite graphs that have an embedding in an orientable surface of genus n which minimally separates the surface of genus n (that is, no proper subset of the embedding separates the genus n surface) but not the surface of genus n-1.

Original entry on oeis.org

1, 4, 21, 191, 3338, 115438
Offset: 0

Views

Author

J. J. P. Veerman, Aug 15 2025

Keywords

Comments

n is called the least separating genus.

Examples

			For genus 0: only the circle.
For genus 1: 2 circles, bouquet of 2 circles, bouquet of 3 circles, 4-fold multi-edge.

References

  • C. N. Aagaard and J. J. P. Veerman, Classification of Minimal Separating Sets of Low Genus Surfaces, Topology and its Applications, Accepted, 2025.
  • J. Bernhard and J. J. P. Veerman, The Topology of Surface Mediatrices, Topology and its Applications, 154, 54-68, 2007.

Crossrefs

Cf. A384639, A387067, A387068.

A387068 Number of equivalence classes (up to homeomorphism) of finite, connected ribbon graphs that have an embedding in an orientable surface of genus n which minimally separates the surface of genus n (that is, no proper subset of the embedding separates the genus n surface) but not the surface of genus n-1.

Original entry on oeis.org

1, 3, 31, 1831, 462638, 243066565
Offset: 0

Views

Author

J. J. P. Veerman, Aug 15 2025

Keywords

Comments

n is called the least separating genus.
These numbers are larger than those of A387067, because different embeddings of the same graph are counted separately. For instance, there is a ribbon graph for the bouquet of 3 circles with least separating genus 1 and a different embedding with least separating genus 2.

Examples

			For genus 0: thickened circle.
For genus 1: thickened versions of a bouquet of 2 circles, bouquet of 3 circles, 4-fold multi-edge.

References

  • C. N. Aagaard and J. J. P. Veerman, Classification of Minimal Separating Sets of Low Genus Surfaces, Topology and its Applications, Accepted, 2025.

Crossrefs

Cf. A384639, A387066, A387067.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.