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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..19.

Gus Wiseman, Unlabeled graphs with 5 vertices, organized by non-spanning edge-connectivity (isolated vertices not shown).

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.

Cf. A322338, A322396, A326787, A327069, A327077, A327097, A327099, A327102, A327200, A327231.

Sequence in context: A116464 A284532 A125585 * A191860 A109973 A340488

Adjacent sequences:  A327233 A327234 A327235 * A327237 A327238 A327239

KEYWORD

nonn,tabf,more

AUTHOR

Gus Wiseman, Sep 03 2019

STATUS

approved

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