A327363 - OEIS

%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