cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A327200 Number of labeled graphs with n vertices and non-spanning edge-connectivity >= 2.

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%I A327200 #5 Sep 01 2019 22:04:34
%S A327200 0,0,0,4,42,718,26262,1878422,256204460,67525498676,34969833809892,
%T A327200 35954978661632864,73737437034063350534,302166248212488958298674,
%U A327200 2475711390267267917290354410,40563960064630744031043287569378,1329219366981359393514586291328267704
%N A327200 Number of labeled graphs with n vertices and non-spanning edge-connectivity >= 2.
%C A327200 The non-spanning edge-connectivity of a graph is the minimum number of edges that must be removed to obtain a graph whose edge-set is disconnected or empty.
%H A327200 Gus Wiseman, <a href="/A327200/a327200.png">The a(4) = 42 graphs with non-spanning edge-connectivity >= 2.</a>
%F A327200 Binomial transform of A322395, if we assume A322395(0) = A322395(1) = A322395(2) = 0.
%t A327200 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]]]]]]]]];
%t A327200 eConn[sys_]:=If[Length[csm[sys]]!=1,0,Length[sys]-Max@@Length/@Select[Union[Subsets[sys]],Length[csm[#]]!=1&]];
%t A327200 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],eConn[#]>=2&]],{n,0,5}]
%Y A327200 Row sums of A327148 if the first two columns are removed.
%Y A327200 BII-numbers of set-systems with non-spanning edge-connectivity >= 2 are A327102.
%Y A327200 Graphs with non-spanning edge-connectivity 1 are A327231.
%Y A327200 Cf. A001187, A006129, A095983, A182100, A322395, A326787, A327076, A327079, A327097, A327099, A327236.
%K A327200 nonn
%O A327200 0,4
%A A327200 _Gus Wiseman_, Sep 01 2019