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A327069 Triangle read by rows where T(n,k) is the number of labeled simple graphs with n vertices and spanning edge-connectivity k. 24
1, 1, 0, 1, 1, 0, 4, 3, 1, 0, 26, 28, 9, 1, 0, 296, 475, 227, 25, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..20.

EXAMPLE

Triangle begins:

    1

    1   0

    1   1   0

    4   3   1   0

   26  28   9   1   0

  296 475 227  25   1   0

MATHEMATICA

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}]

CROSSREFS

Row sums are A006125.

Column k = 0 is A054592, if we assume A054592(1) = 1.

Column k = 1 is A327071.

Column k = 2 is A327146.

The unlabeled version (except with offset 1) is A263296.

Cf. A001187, A095983, A259862, A322338, A326787, A327070, A327072, A327073.

Sequence in context: A083904 A215861 A327366 * A327334 A195596 A332054

Adjacent sequences:  A327066 A327067 A327068 * A327070 A327071 A327072

KEYWORD

nonn,tabl,more

AUTHOR

Gus Wiseman, Aug 23 2019

STATUS

approved

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Last modified February 24 18:55 EST 2021. Contains 341584 sequences. (Running on oeis4.)