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A327236
Irregular triangle read by rows with trailing zeros removed where T(n,k) is the number of unlabeled simple graphs with n vertices whose edge-set has non-spanning edge-connectivity k.
11
1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 1, 4, 5, 10, 8, 5, 1, 1
OFFSET
0,9
COMMENTS
The non-spanning edge-connectivity of a graph is the minimum number of edges that must be removed to obtain a disconnected or empty graph, ignoring isolated vertices.
EXAMPLE
Triangle begins:
1
1
1 1
1 1 1 1
2 2 3 3 1
4 5 10 8 5 1 1
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]]]]]]]]];
edgeConnSys[sys_]:=If[Length[csm[sys]]!=1, 0, Length[sys]-Max@@Length/@Select[Union[Subsets[sys]], Length[csm[#]]!=1&]];
Table[Length[Union[normclut/@Select[Subsets[Subsets[Range[n], {2}]], edgeConnSys[#]==k&]]], {n, 0, 5}, {k, 0, Binomial[n, 2]}]//.{foe___, 0}:>{foe}
CROSSREFS
Row sums are A000088.
Column k = 0 is A327235.
The labeled version is A327148.
The covering version is A327201.
Spanning edge-connectivity is A263296.
Vertex-connectivity is A259862.
Sequence in context: A346136 A284532 A125585 * A191860 A109973 A340488
KEYWORD
nonn,tabf,more
AUTHOR
Gus Wiseman, Sep 03 2019
STATUS
approved