A327146 Number of labeled simple graphs with n vertices and spanning edge-connectivity 2.

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.

Links

Table of n, a(n) for n=0..5.

Gus Wiseman, The a(4) = 9 simple graphs with spanning edge-connectivity 2.

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.

Cf. A006129, A327070, A327071, A327102, A327109, A327111, A327129, A327144.

Sequence in context: A218536 A338377 A211048 * A158728 A197406 A197428

Adjacent sequences: A327143 A327144 A327145 * A327147 A327148 A327149

Keyword

nonn,more

Author

Gus Wiseman, Aug 27 2019

Status

approved