OFFSET
0,4
COMMENTS
The cut-connectivity of a graph is the minimum number of vertices that must be removed (along with any empty or duplicate edges) to obtain a disconnected or empty graph.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
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]]]]]]]]];
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}]], Union@@#==Range[n]&&cutConnSys[Range[n], #]==1&]], {n, 0, 3}]
PROG
(PARI) seq(n)={my(g=log(sum(k=0, n, 2^binomial(k, 2) * x^k / k!) + O(x*x^n))); Vec(serlaplace(g-intformal(1+log(x/serreverse(x*deriv(g))))), -(n+1))} \\ Andrew Howroyd, Sep 11 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 25 2019
STATUS
approved