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

4,13

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

Table of n, a(n) for n=4..27.

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.

Sequence in context: A355367 A355403 A319055 * A007894 A102625 A117777

Adjacent sequences: A339543 A339544 A339545 * A339547 A339548 A339549

Keyword

nonn,more

Author

Hugo Pfoertner, Dec 08 2020

Status

approved