%I #4 Sep 26 2019 15:24:43
%S 1,1,0,2,1,0,8,4,1,0,64,38,10,1,0,1024,728,238,26,1,0
%N Triangle read by rows where T(n,k) is the number of labeled simple graphs with n vertices and vertex-connectivity >= k.
%C The vertex-connectivity of a graph is the minimum number of vertices that must be removed (along with any incident edges) to obtain a non-connected graph or singleton.
%e Triangle begins:
%e 1
%e 1 0
%e 2 1 0
%e 8 4 1 0
%e 64 38 10 1 0
%e 1024 728 238 26 1 0
%t 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 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],vertConnSys[Range[n],#]>=k&]],{n,0,4},{k,0,n}]
%Y Column k = 0 is A006125.
%Y Column k = 1 is A001187.
%Y Column k = 2 is A013922.
%Y The unlabeled version is A327805.
%Y Row-wise partial sums of A327334 (vertex-connectivity exactly k).
%Y Cf. A259862, A327114, A327125, A327126, A327127, A327806.
%K nonn,tabl,more
%O 0,4
%A _Gus Wiseman_, Sep 26 2019