OFFSET
0,7
COMMENTS
We define the cut-connectivity of a graph to be the minimum number of vertices that must be removed (along with any incident edges) to obtain a disconnected or empty graph, with the exception that a graph with one vertex and no edges has cut-connectivity 1. Except for complete graphs, this is the same as vertex-connectivity.
EXAMPLE
Triangle begins:
1
0 1
1 0 1
4 3 0 1
26 28 9 0 1
296 490 212 25 0 1
MATHEMATICA
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];
cutConnSys[vts_, eds_]:=If[Length[vts]==1, 1, Min@@Length/@Select[Subsets[vts], Function[del, csm[DeleteCases[DeleteCases[eds, Alternatives@@del, {2}], {}]]!={Complement[vts, del]}]]];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], cutConnSys[Range[n], #]==k&]], {n, 0, 4}, {k, 0, n}]
CROSSREFS
KEYWORD
AUTHOR
Gus Wiseman, Aug 25 2019
EXTENSIONS
a(21)-a(28) from Robert Price, May 20 2021
a(1) and a(2) corrected by Robert Price, May 20 2021
STATUS
approved