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 A326293 Number of non-nesting, topologically connected simple graphs with vertices {1..n}. 16
 1, 1, 2, 4, 8, 27, 192, 1750 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Two edges {a,b}, {c,d} are crossing if a < c < b < d or c < a < d < b, and nesting if a < c < d < b or c < a < b < d. A graph with positive integer vertices is topologically connected if the graph whose vertices are the edges and whose edges are crossing pairs of edges is connected. LINKS Table of n, a(n) for n=0..7. Gus Wiseman, The a(5) = 27 non-nesting, topologically connected simple graphs. MATHEMATICA croXQ[eds_]:=MatchQ[eds, {___, {x_, y_}, ___, {z_, t_}, ___}/; x0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]]; Table[Length[Select[Subsets[Subsets[Range[n], {2}]], !nesXQ[#]&&Length[csm[Union[Subsets[#, {1}], Select[Subsets[#, {2}], croXQ]]]]<=1&]], {n, 0, 5}] CROSSREFS The inverse binomial transform is the covering case A326349. Topologically connected simple graphs are A324328. Non-crossing simple graphs are A054726. Topologically connected set partitions are A099947. Cf. A000108, A000699, A006125, A007297, A117662, A136653. Cf. A324173, A324323, A324327, A326244, A326330, A326341. Sequence in context: A037170 A212409 A006399 * A324328 A056800 A302915 Adjacent sequences: A326290 A326291 A326292 * A326294 A326295 A326296 KEYWORD nonn,more AUTHOR Gus Wiseman, Jun 29 2019 STATUS approved

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Last modified July 24 02:09 EDT 2024. Contains 374575 sequences. (Running on oeis4.)