cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A327363 Triangle read by rows where T(n,k) is the number of labeled simple graphs with n vertices and vertex-connectivity >= k.

This page as a plain text file.
%I A327363 #4 Sep 26 2019 15:24:43
%S A327363 1,1,0,2,1,0,8,4,1,0,64,38,10,1,0,1024,728,238,26,1,0
%N A327363 Triangle read by rows where T(n,k) is the number of labeled simple graphs with n vertices and vertex-connectivity >= k.
%C A327363 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 A327363 Triangle begins:
%e A327363      1
%e A327363      1    0
%e A327363      2    1    0
%e A327363      8    4    1    0
%e A327363     64   38   10    1    0
%e A327363   1024  728  238   26    1    0
%t A327363 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 A327363 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],vertConnSys[Range[n],#]>=k&]],{n,0,4},{k,0,n}]
%Y A327363 Column k = 0 is A006125.
%Y A327363 Column k = 1 is A001187.
%Y A327363 Column k = 2 is A013922.
%Y A327363 The unlabeled version is A327805.
%Y A327363 Row-wise partial sums of A327334 (vertex-connectivity exactly k).
%Y A327363 Cf. A259862, A327114, A327125, A327126, A327127, A327806.
%K A327363 nonn,tabl,more
%O A327363 0,4
%A A327363 _Gus Wiseman_, Sep 26 2019