The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A326787

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A326787

Non-spanning edge-connectivity of the set-system with BII-number n.
(history; published version)

#10 by Bruno Berselli at Thu Sep 26 03:43:10 EDT 2019

STATUS

reviewed

#9 by Joerg Arndt at Thu Sep 26 02:34:11 EDT 2019

STATUS

proposed

#8 by Gus Wiseman at Wed Sep 25 01:52:07 EDT 2019

STATUS

editing

#7 by Gus Wiseman at Tue Sep 24 18:00:09 EDT 2019

NAME

Edge-connectivity of the set-system with BII-number n.

COMMENTS

Elements of a set-system are sometimes called edges. The edge-connectivity of a set-system is the minimum number of edges that must be removed to result in a disconnected (or empty) set-system.

LINKS

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]]]]]]]]];

edgeConn[y_]:=If[Length[csm[bpe/@y]]!=1, 0, Length[y]-Max@@Length/@Select[Union[Subsets[y]], Length[csm[bpe/@#]]!=1&]];

Table[edgeConn[bpe[n]], {n, 0, 100}]

STATUS

approved

Discussion

Tue Sep 24

18:00

Gus Wiseman: Updated for the non-spanning/spanning distinction. No change to data.

#6 by N. J. A. Sloane at Sat Jul 27 14:57:51 EDT 2019

COMMENTS

A binary index of n is any position of a 1 in its reversed binary digits. The binary indices of n are row n of A048793. We define the set-system with BII-number n to be obtained by taking the binary indices of each binary index of n. Every finite set of finite nonempty sets has a different BII-number. For example, 18 has reversed binary digits (0,1,0,0,1), and since the binary indices of 2 and 5 are {2} and {1,3} respectively, the BII-number of {{2},{1,3}} is 18.

Discussion

Sat Jul 27

14:57

OEIS Server: https://oeis.org/edit/global/2822

#5 by Susanna Cuyler at Thu Jul 25 20:58:49 EDT 2019

STATUS

proposed

#4 by Gus Wiseman at Thu Jul 25 13:57:21 EDT 2019

STATUS

editing

#3 by Gus Wiseman at Thu Jul 25 13:57:15 EDT 2019

CROSSREFS

Cf. A000120, A013922, A048793, A070939, A095983, A322336, A322337, A322338 (same for MM-numbers), A326031, A326749, A326753, A326786 (vertex-connectivity).

#2 by Gus Wiseman at Thu Jul 25 06:21:42 EDT 2019

NAME

allocated for Gus Wiseman

DATA

OFFSET

COMMENTS

EXAMPLE

MATHEMATICA

CROSSREFS

KEYWORD

allocated

AUTHOR

STATUS

approved

#1 by Gus Wiseman at Wed Jul 24 03:37:43 EDT 2019

NAME

KEYWORD

STATUS