OFFSET
0,4
COMMENTS
A bridge is an edge whose removal disconnected the graph, while an endpoint is a vertex belonging to only one edge. The non-spanning edge-connectivity of a graph is the minimum number of edges that must be removed to obtain a graph whose edge-set is disconnected or empty.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..50
FORMULA
Binomial transform of A327079.
EXAMPLE
The a(2) = 1 through a(4) = 18 edge-sets:
{12} {12} {12}
{13} {13}
{23} {14}
{23}
{24}
{34}
{12,13,24}
{12,13,34}
{12,14,23}
{12,14,34}
{12,23,34}
{12,24,34}
{13,14,23}
{13,14,24}
{13,23,24}
{13,24,34}
{14,23,24}
{14,23,34}
MATHEMATICA
csm[s_]:=With[{c=Select[Subsets[Range[Length[s]], {2}], 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[#]==1&]], {n, 0, 4}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 01 2019
EXTENSIONS
Terms a(6) and beyond from Andrew Howroyd, Sep 11 2019
STATUS
approved