|
|
A327363
|
|
Triangle read by rows where T(n,k) is the number of labeled simple graphs with n vertices and vertex-connectivity >= k.
|
|
1
|
|
|
1, 1, 0, 2, 1, 0, 8, 4, 1, 0, 64, 38, 10, 1, 0, 1024, 728, 238, 26, 1, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
The vertex-connectivity of a graph is the minimum number of vertices that must be removed (along with any incident edges) to obtain a non-connected graph or singleton.
|
|
LINKS
|
|
|
EXAMPLE
|
Triangle begins:
1
1 0
2 1 0
8 4 1 0
64 38 10 1 0
1024 728 238 26 1 0
|
|
MATHEMATICA
|
vertConnSys[vts_, eds_]:=Min@@Length/@Select[Subsets[vts], Function[del, Length[del]==Length[vts]-1||csm[DeleteCases[DeleteCases[eds, Alternatives@@del, {2}], {}]]!={Complement[vts, del]}]];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], vertConnSys[Range[n], #]>=k&]], {n, 0, 4}, {k, 0, n}]
|
|
CROSSREFS
|
Row-wise partial sums of A327334 (vertex-connectivity exactly k).
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|