A327146 - OEIS

%I #5 Sep 01 2019 08:39:54

%S 0,0,0,1,9,227

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

%C 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.

%H Gus Wiseman, <a href="/A327146/a327146.png">The a(4) = 9 simple graphs with spanning edge-connectivity 2.</a>

%t 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]]]]]]]]];

%t spanEdgeConn[vts_,eds_]:=Length[eds]-Max@@Length/@Select[Subsets[eds],Union@@#!=vts||Length[csm[#]]!=1&];

%t Table[Length[Select[Subsets[Subsets[Range[n],{2}]],spanEdgeConn[Range[n],#]==2&]],{n,0,4}]

%Y Column k = 2 of A327069.

%Y BII-numbers of set-systems with spanning edge-connectivity 2 are A327108.

%Y The generalization to set-systems is A327130.

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

%K nonn,more

%O 0,5

%A _Gus Wiseman_, Aug 27 2019