OFFSET
0,4
COMMENTS
A graph is covering if the vertex set is the union of the edge set, so there are no isolated vertices.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
FORMULA
Inverse binomial transform of A327364.
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]]]]]]]]];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], Union@@#==Range[n]&&Length[csm[#]]==1&&Min@@Length/@Split[Sort[Join@@#]]==1&]], {n, 0, 5}]
PROG
(PARI) seq(n)={Vec(serlaplace(-x^2/2 + log(sum(k=0, n, 2^binomial(k, 2)*x^k/k! + O(x*x^n))) - log(sum(k=0, n, 2^binomial(k, 2)*(x*exp(-x + O(x^n)))^k/k!))), -(n+1))} \\ Andrew Howroyd, Sep 11 2019
CROSSREFS
The non-connected version is A327227.
The non-covering version is A327364.
Graphs with endpoints are A245797.
Connected covering graphs are A001187.
Connected graphs with bridges are A327071.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 04 2019
EXTENSIONS
Terms a(7) and beyond from Andrew Howroyd, Sep 11 2019
STATUS
approved