A326331 Number of simple graphs covering the vertices {1..n} whose nesting edges are connected.

1, 0, 1, 0, 1, 14, 539

Offset: 0

Author

Gus Wiseman, Jun 27 2019

Keywords

• nonn
• more

Comments

Covering means there are no isolated vertices. 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) = 14 simple nesting-connected covering graphs.

Crossrefs

The non-covering case is the binomial transform A326330.

Covering graphs whose crossing edges are connected are A324327.

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}]],Union@@#==Range[n]&&Length[nestcmpts[#]]<=1&]],{n,0,5}]