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A327069
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Triangle read by rows where T(n,k) is the number of labeled simple graphs with n vertices and spanning edge-connectivity k.
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24
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1, 1, 0, 1, 1, 0, 4, 3, 1, 0, 26, 28, 9, 1, 0, 296, 475, 227, 25, 1, 0, 6064, 14736, 10110, 1782, 75, 1, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,7
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COMMENTS
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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.
We consider a graph with one vertex and no edges to be disconnected.
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LINKS
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EXAMPLE
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Triangle begins:
1
1 0
1 1 0
4 3 1 0
26 28 9 1 0
296 475 227 25 1 0
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MATHEMATICA
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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]]]]]]]]];
spanEdgeConn[vts_, eds_]:=Length[eds]-Max@@Length/@Select[Subsets[eds], Union@@#!=vts||Length[csm[#]]!=1&];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], spanEdgeConn[Range[n], #]==k&]], {n, 0, 5}, {k, 0, n}]
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CROSSREFS
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The unlabeled version (except with offset 1) is A263296.
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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