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

%I A355638 #8 Jul 11 2022 16:04:32
%S A355638 1,0,1,1,1,1,2,2,4,5,7,10,16,27,42,67,116,187,329,570,970,1723,3021,
%T A355638 5338,9563,16981,30517,54913,98847,179119,324333,589059,1072997,
%U A355638 1955207,3573129,6538088
%N A355638 Number of polyhedra (3-polytopes) of graph radius 1 on n edges.
%C A355638 Data was gathered with the help of Scientific IT & Application Support (SCITAS) High Performance Computing (HPC) for the EPFL community.
%H A355638 R. W. Maffucci, <a href="https://arxiv.org/abs/2207.02040">On unigraphic 3-polytopes of radius one</a>, arXiv:2207.02040 [math.CO], 2022.
%e A355638 For n=6 there is only the tetrahedron, n=8 the square pyramid, n=9 the triangular bipyramid,...
%t A355638 Needs["IGraphM`"]
%t A355638 ra[8]:={Square pyramid}
%t A355638 ra[q]=opb[ra[q-1]]
%t A355638 opb[setg_] :=
%t A355638 Prepend[DeleteDuplicatesBy[
%t A355638    Flatten[Table[
%t A355638      EdgeAdd[g, UndirectedEdge[x[[1]], x[[2]]],
%t A355638       GraphLayout -> "TutteEmbedding"], {g, setg}, {x,
%t A355638       Flatten[Table[
%t A355638         Complement[Subsets[i, {2}],
%t A355638          Table[{i[[j]], i[[j + 1]]}, {j, Length[i] - 1}], {{i[[1]],
%t A355638            i[[-1]]}}], {i, Select[IGFaces[g], Length[#] > 3 &]}],
%t A355638        1]}]], CanonicalGraph],
%t A355638   If[OddQ[EdgeCount[setg[[1]]]],
%t A355638    WheelGraph[EdgeCount[setg[[1]]]/2 + 3/2,
%t A355638     GraphLayout -> "TutteEmbedding", ImageSize -> 25], Nothing]]
%Y A355638 Cf. A002840.
%K A355638 nonn,more
%O A355638 6,7
%A A355638 _Riccardo Maffucci_, Jul 11 2022