A326349 Number of non-nesting, topologically connected simple graphs covering {1..n}.

1, 0, 1, 0, 1, 11, 95, 797

Offset: 0

Author

Gus Wiseman, Jun 30 2019

Keywords

• nonn
• more

Comments

Covering means there are no isolated vertices. 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.

Examples

			The a(5) = 11 edge-sets:
  {13,14,25}
  {13,24,25}
  {13,24,35}
  {14,24,35}
  {14,25,35}
  {13,14,24,25}
  {13,14,24,35}
  {13,14,25,35}
  {13,24,25,35}
  {14,24,25,35}
  {13,14,24,25,35}
		

Links

• Gus Wiseman, The a(6) = 95 non-nesting, topologically connected, covering simple graphs.

Crossrefs

The binomial transform is the non-covering case A326293.

Topologically connected, covering simple graphs are A324327.

Non-crossing, covering simple graphs are A324169.

Cf. A000108, A000699, A006125, A054726, A099947, A117662.

Cf. A324323, A324328, A326329, A326330, A326339, A326341.

Programs

Mathematica

croXQ[eds_]:=MatchQ[eds,{_,{x_,y_},_,{z_,t_},_}/;x_,{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}]],Union@@#==Range[n]&&!nesXQ[#]&&Length[csm[Union[Subsets[#,{1}],Select[Subsets[#,{2}],croXQ]]]]<=1&]],{n,0,5}]