A327199 Number of labeled simple graphs with n vertices whose edge-set is not connected.

1, 1, 1, 1, 4, 56, 1031, 27189, 1165424, 89723096, 13371146135, 3989665389689, 2388718032951812, 2852540291841718752, 6768426738881535155247, 31870401029679493862010949, 297787425565749788134314214272

Offset: 0

Author

Gus Wiseman, Sep 01 2019

Keywords

• nonn

Comments

Also graphs with non-spanning edge-connectivity 0.

Examples

			The a(4) = 4 edge-sets: {}, {12,34}, {13,24}, {14,23}.
		

Crossrefs

Column k = 0 of A327148.

The covering case is A327070.

The unlabeled version is A327235.

Cf. A001187, A006129, A322395, A326787, A327075, A327076, A327079, A327129, A327200, A327201, A327231, A327236.

Programs

Mathematica

csm[s_]:=With[{c=Select[Subsets[Range[Length[s]],{2}],Length[Intersection@@s[[#]]]>0&]},If[c=={},s,csm[Sort[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
Table[Length[Select[Subsets[Subsets[Range[n],{2}]],Length[csm[#]]!=1&]],{n,0,5}]

Formula

Binomial transform of A327070.