login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons 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

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

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.

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

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 29 04:33 EDT 2020. Contains 334697 sequences. (Running on oeis4.)