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

0, 0, 0, 1, 9, 227

Offset: 0

Author

Gus Wiseman, Aug 27 2019

Keywords

• nonn
• more

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

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

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.

Programs

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}]