OFFSET
0,6
COMMENTS
The non-spanning edge-connectivity of a graph is the minimum number of edges that must be removed (along with any isolated vertices) to obtain a disconnected or empty graph.
FORMULA
EXAMPLE
Triangle begins:
1
1
1 1
1 3 3 1
4 18 27 14 1
56 250 402 240 65 10 1
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]]]]]]]]];
edgeConnSys[sys_]:=If[Length[csm[sys]]!=1, 0, Length[sys]-Max@@Length/@Select[Union[Subsets[sys]], Length[csm[#]]!=1&]];
Table[Length[Select[Subsets[Subsets[Range[n], {2}]], edgeConnSys[#]==k&]], {n, 0, 4}, {k, 0, Binomial[n, 2]}]//.{foe___, 0}:>{foe}
CROSSREFS
Row sums are A006125.
Column k = 0 is A327199.
Column k = 1 is A327231.
The corresponding triangle for vertex-connectivity is A327125.
The corresponding triangle for spanning edge-connectivity is A327069.
The covering version is A327149.
KEYWORD
nonn,tabf,more
AUTHOR
Gus Wiseman, Aug 27 2019
EXTENSIONS
a(20)-a(28) from Robert Price, May 25 2021
STATUS
approved