A326330 Number of simple graphs with vertices {1..n} whose nesting edges are connected.

1, 1, 2, 4, 8, 30, 654

Offset: 0

Author

Gus Wiseman, Jun 27 2019

Keywords

• nonn
• more

Comments

Two edges {a,b}, {c,d} are nesting if a < c < d < b or c < a < b < d. A graph has its nesting edges connected if the graph whose vertices are the edges and whose edges are nesting pairs of edges is connected.

Links

• Gus Wiseman, The a(5) = 30 nesting-connected simple graphs.

Crossrefs

The covering case is the inverse binomial transform A326331.

Graphs whose crossing edges are connected are A324328.

Cf. A006125, A007297, A054726, A099947, A117662, A136653, A324328.

Cf. A326210, A326293, A326335, A326336, A326337, A326338, A326339.

Programs

Mathematica

nesXQ[stn_]:=MatchQ[stn,{_,{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}]],Length[nestcmpts[#]]<=1&]],{n,0,5}]