|
| |
|
|
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
|
| |
|
|
