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A327199
Number of labeled simple graphs with n vertices whose edge-set is not connected.
5
1, 1, 1, 1, 4, 56, 1031, 27189, 1165424, 89723096, 13371146135, 3989665389689, 2388718032951812, 2852540291841718752, 6768426738881535155247, 31870401029679493862010949, 297787425565749788134314214272
OFFSET
0,5
COMMENTS
Also graphs with non-spanning edge-connectivity 0.
FORMULA
Binomial transform of A327070.
EXAMPLE
The a(4) = 4 edge-sets: {}, {12,34}, {13,24}, {14,23}.
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}]
CROSSREFS
Column k = 0 of A327148.
The covering case is A327070.
The unlabeled version is A327235.
Sequence in context: A369534 A078533 A299302 * A358886 A371678 A009058
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 01 2019
STATUS
approved