A339546 Number of at least 3-connected planar triangulations on n vertices such that the minimum valence of any vertex in the mesh is maximized and the number of vertices with this minimum valence is minimized.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 6, 6, 15, 17, 40, 45, 89, 116, 199, 271

Offset: 4

Author

Hugo Pfoertner, Dec 08 2020

Keywords

• nonn
• more

Comments

It is conjectured that for a polyhedron with maximum possible volume inscribed in a sphere the stated condition is necessary. All known polyhedra with conjecturally maximum volume satisfy this condition. For n <= 15 the given condition determines a unique mesh topology for each n, which coincides with the proved optimal solutions for n <= 8.

References

• See A081314 for references and links.

Links

• Gunnar Brinkmann and Brendan McKay, plantri and fullgen programs for generation of certain types of planar graph.
• Hugo Pfoertner, Construction of sequence, table of vertex degrees of triangulations (2020).

Crossrefs

Cf. A081314, A081621, A339260, A339261, A339262, A339263.