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

0, 0, 0, 4, 42, 718, 26262, 1878422, 256204460, 67525498676, 34969833809892, 35954978661632864, 73737437034063350534, 302166248212488958298674, 2475711390267267917290354410, 40563960064630744031043287569378, 1329219366981359393514586291328267704

Offset: 0

Author

Gus Wiseman, Sep 01 2019

Keywords

• nonn

Comments

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.

Links

• Gus Wiseman, The a(4) = 42 graphs with non-spanning edge-connectivity >= 2.

Crossrefs

Row sums of A327148 if the first two columns are removed.

BII-numbers of set-systems with non-spanning edge-connectivity >= 2 are A327102.

Graphs with non-spanning edge-connectivity 1 are A327231.

Cf. A001187, A006129, A095983, A182100, A322395, A326787, A327076, A327079, A327097, A327099, A327236.

Programs

Mathematica

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]]]]]]]]];
eConn[sys_]:=If[Length[csm[sys]]!=1,0,Length[sys]-Max@@Length/@Select[Union[Subsets[sys]],Length[csm[#]]!=1&]];
Table[Length[Select[Subsets[Subsets[Range[n],{2}]],eConn[#]>=2&]],{n,0,5}]

Formula

Binomial transform of A322395, if we assume A322395(0) = A322395(1) = A322395(2) = 0.