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A327236
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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.
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11
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1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 1, 4, 5, 10, 8, 5, 1, 1
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history;
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internal format)
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OFFSET
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0,9
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COMMENTS
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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.
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LINKS
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EXAMPLE
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Triangle begins:
1
1
1 1
1 1 1 1
2 2 3 3 1
4 5 10 8 5 1 1
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MATHEMATICA
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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}
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CROSSREFS
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Spanning edge-connectivity is A263296.
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KEYWORD
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nonn,tabf,more
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AUTHOR
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STATUS
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approved
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