A355638 Number of polyhedra (3-polytopes) of graph radius 1 on n edges.

1, 0, 1, 1, 1, 1, 2, 2, 4, 5, 7, 10, 16, 27, 42, 67, 116, 187, 329, 570, 970, 1723, 3021, 5338, 9563, 16981, 30517, 54913, 98847, 179119, 324333, 589059, 1072997, 1955207, 3573129, 6538088

Offset

6,7

Comments

Data was gathered with the help of Scientific IT & Application Support (SCITAS) High Performance Computing (HPC) for the EPFL community.

Links

Table of n, a(n) for n=6..41.

R. W. Maffucci, On unigraphic 3-polytopes of radius one, arXiv:2207.02040 [math.CO], 2022.

Example

For n=6 there is only the tetrahedron, n=8 the square pyramid, n=9 the triangular bipyramid,...

Mathematica

Needs["IGraphM`"]
ra[8]:={Square pyramid}
ra[q]=opb[ra[q-1]]
opb[setg_] :=
Prepend[DeleteDuplicatesBy[
   Flatten[Table[
     EdgeAdd[g, UndirectedEdge[x[[1]], x[[2]]],
      GraphLayout -> "TutteEmbedding"], {g, setg}, {x,
      Flatten[Table[
        Complement[Subsets[i, {2}],
         Table[{i[[j]], i[[j + 1]]}, {j, Length[i] - 1}], {{i[[1]],
           i[[-1]]}}], {i, Select[IGFaces[g], Length[#] > 3 &]}],
       1]}]], CanonicalGraph],
  If[OddQ[EdgeCount[setg[[1]]]],
   WheelGraph[EdgeCount[setg[[1]]]/2 + 3/2,
    GraphLayout -> "TutteEmbedding", ImageSize -> 25], Nothing]]

Crossrefs

Cf. A002840.

Sequence in context: A241736 A034398 A277062 * A027069 A238494 A359388

Adjacent sequences: A355635 A355636 A355637 * A355639 A355640 A355641

Keyword

nonn,more

Author

Riccardo Maffucci, Jul 11 2022

Status

approved