

A327196


Number of connected setsystems with n vertices and at least one bridge that is not an endpoint (nonspanning edgeconnectivity 1).


3




OFFSET

0,3


COMMENTS

A setsystem is a finite set of finite nonempty sets. Elements of a setsystem are sometimes called edges. The nonspanning edgeconnectivity of a setsystem is the minimum number of edges that must be removed (along with any noncovered vertices) to obtain a disconnected or empty setsystem.


LINKS

Table of n, a(n) for n=0..4.


FORMULA

Binomial transform of A327129.


EXAMPLE

Nonisomorphic representatives of the a(3) = 44 setsystems:
{{1}}
{{1,2}}
{{1,2,3}}
{{1},{2},{1,2}}
{{1},{1,2},{2,3}}
{{1},{2},{1,2,3}}
{{1},{2,3},{1,2,3}}
{{1},{2},{1,2},{1,3}}
{{1},{2},{1,3},{2,3}}
{{1},{2},{3},{1,2,3}}
{{1},{2},{1,3},{1,2,3}}
{{1},{2},{3},{1,2},{1,3}}
{{1},{2},{3},{1,2},{1,2,3}}


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]]]]]]]]];
eConn[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], {1, n}]], eConn[#]==1&]], {n, 0, 3}]


CROSSREFS

The covering version is A327129.
The BIInumbers of these setsystems are A327099.
The restriction to simple graphs is A327231.
Setsystems with spanning edgeconnectivity 1 are A327145.
Cf. A263296, A322395, A327079, A327111, A327148, A327149, A327200.
Sequence in context: A224784 A243221 A238816 * A024254 A167781 A173327
Adjacent sequences: A327193 A327194 A327195 * A327197 A327198 A327199


KEYWORD

nonn,more


AUTHOR

Gus Wiseman, Aug 31 2019


STATUS

approved



