OFFSET
0,4
COMMENTS
Same as A327114 except a(2) = 1.
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.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
EXAMPLE
The a(2) = 1 through a(4) = 28 edge-sets:
{12} {12,13} {12,13,14}
{12,23} {12,13,24}
{13,23} {12,13,34}
{12,14,23}
{12,14,34}
{12,23,24}
{12,23,34}
{12,24,34}
{13,14,23}
{13,14,24}
{13,23,24}
{13,23,34}
{13,24,34}
{14,23,24}
{14,23,34}
{14,24,34}
{12,13,14,23}
{12,13,14,24}
{12,13,14,34}
{12,13,23,24}
{12,13,23,34}
{12,14,23,24}
{12,14,24,34}
{12,23,24,34}
{13,14,23,34}
{13,14,24,34}
{13,23,24,34}
{14,23,24,34}
MATHEMATICA
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]]]]]]]]];
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]}]];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], vertConnSys[Range[n], #]==1&]], {n, 0, 4}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 02 2019
EXTENSIONS
Terms a(6) and beyond from Andrew Howroyd, Sep 11 2019
STATUS
approved