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A327198
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Number of labeled simple graphs covering n vertices with vertex-connectivity 2.
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7
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0, 0, 0, 1, 9, 212, 9600, 789792, 114812264, 29547629568, 13644009626400, 11489505388892800, 17918588321874717312, 52482523149603539181312, 292311315623259148521270784, 3129388799344153886272170009600, 64965507855114369076680860799267840
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OFFSET
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0,5
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COMMENTS
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The vertex-connectivity of a set-system is the minimum number of vertices that must be removed (along with any resulting empty edges) to obtain a non-connected set-system or singleton. Note that this means a single node has vertex-connectivity 0.
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LINKS
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FORMULA
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MATHEMATICA
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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]]]]]]]]];
vertConnSys[vts_, eds_]:=Min@@Length/@Select[Subsets[vts], Function[del, Length[del]==Length[vts]-1||csm[DeleteCases[DeleteCases[eds, Alternatives@@del, {2}], {}]]!={Complement[vts, del]}]];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], vertConnSys[Range[n], #]==2&]], {n, 0, 5}]
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CROSSREFS
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Cf. A005644, A013922, A052442, A259862, A326786, A327082, A327101, A327112, A327113, A327126, A327227.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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