A327069 - OEIS

A327069

Triangle read by rows where T(n,k) is the number of labeled simple graphs with n vertices and spanning edge-connectivity k.

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)

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..27.

EXAMPLE

Triangle begins:

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 A354794 A355401

Adjacent sequences: A327066 A327067 A327068 * A327070 A327071 A327072

KEYWORD

nonn,tabl,more

AUTHOR

Gus Wiseman, Aug 23 2019

EXTENSIONS

a(21)-a(27) from Robert Price, May 25 2021

STATUS

approved