cp's OEIS Frontend

A327198 Number of labeled simple graphs covering n vertices with vertex-connectivity 2.

%I A327198 #8 Dec 26 2020 23:53:57
%S A327198 0,0,0,1,9,212,9600,789792,114812264,29547629568,13644009626400,
%T A327198 11489505388892800,17918588321874717312,52482523149603539181312,
%U A327198 292311315623259148521270784,3129388799344153886272170009600,64965507855114369076680860799267840
%N A327198 Number of labeled simple graphs covering n vertices with vertex-connectivity 2.
%C A327198 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.
%H A327198 Andrew Howroyd, <a href="/A327198/b327198.txt">Table of n, a(n) for n = 0..25</a>
%H A327198 Gus Wiseman, <a href="/A327198/a327198.png">The a(4) = 9 simple covering graphs with vertex-connectivity 2.</a>
%F A327198 a(n) = A013922(n) - A005644(n) for n >= 3. - _Andrew Howroyd_, Dec 26 2020
%t A327198 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]]]]]]]]];
%t A327198 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]}]];
%t A327198 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],vertConnSys[Range[n],#]==2&]],{n,0,5}]
%Y A327198 The unlabeled version is A052443.
%Y A327198 Cf. A005644, A013922, A052442, A259862, A326786, A327082, A327101, A327112, A327113, A327126, A327227.
%K A327198 nonn
%O A327198 0,5
%A A327198 _Gus Wiseman_, Sep 01 2019
%E A327198 Terms a(6) and beyond from _Andrew Howroyd_, Dec 26 2020