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.
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
KEYWORD
AUTHOR
Gus Wiseman, Aug 23 2019
EXTENSIONS
a(21)-a(27) from Robert Price, May 25 2021
STATUS
approved