login
A327146
Number of labeled simple graphs with n vertices and spanning edge-connectivity 2.
12
0, 0, 0, 1, 9, 227
OFFSET
0,5
COMMENTS
The spanning edge-connectivity of a graph is the minimum number of edges that must be removed (without removing incident vertices) to obtain a disconnected or empty graph.
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]]]]]]]]];
spanEdgeConn[vts_, eds_]:=Length[eds]-Max@@Length/@Select[Subsets[eds], Union@@#!=vts||Length[csm[#]]!=1&];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], spanEdgeConn[Range[n], #]==2&]], {n, 0, 4}]
CROSSREFS
Column k = 2 of A327069.
BII-numbers of set-systems with spanning edge-connectivity 2 are A327108.
The generalization to set-systems is A327130.
Sequence in context: A218536 A338377 A211048 * A158728 A197406 A197428
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 27 2019
STATUS
approved