login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A327196 Number of connected set-systems with n vertices and at least one bridge that is not an endpoint (non-spanning edge-connectivity 1). 3
0, 1, 4, 44, 2960 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
A set-system is a finite set of finite nonempty sets. Elements of a set-system are sometimes called edges. The non-spanning edge-connectivity of a set-system is the minimum number of edges that must be removed (along with any non-covered vertices) to obtain a disconnected or empty set-system.
LINKS
FORMULA
Binomial transform of A327129.
EXAMPLE
Non-isomorphic representatives of the a(3) = 44 set-systems:
{{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 BII-numbers of these set-systems are A327099.
The restriction to simple graphs is A327231.
Set-systems with spanning edge-connectivity 1 are A327145.
Sequence in context: A224784 A243221 A238816 * A024254 A167781 A173327
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 31 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)