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A327234 Smallest BII-number of a set-system with cut-connectivity n. 1
0, 1, 4, 52, 2868 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
A binary index of n is any position of a 1 in its reversed binary expansion. 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 set-system (finite set of finite nonempty sets) has a different BII-number. For example, 18 has reversed binary expansion (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. Elements of a set-system are sometimes called edges.
We define the cut-connectivity (A326786) of a set-system to be the minimum number of vertices that must be removed (along with any resulting empty edges) to obtain a disconnected or empty set-system, with the exception that a set-system with one vertex has cut-connectivity 1. Except for cointersecting set-systems (A326853), this is the same as vertex-connectivity (A327051).
Conjecture: a(n > 1) = A327373(n) = the BII-number of K_n.
LINKS
EXAMPLE
The sequence of terms together with their corresponding set-systems:
0: {}
1: {{1}}
4: {{1,2}}
52: {{1,2},{1,3},{2,3}}
2868: {{1,2},{1,3},{2,3},{1,4},{2,4},{3,4}}
CROSSREFS
The same for spanning edge-connectivity is A327147.
The cut-connectivity of the set-system with BII-number n is A326786(n).
Sequence in context: A015001 A355612 A317829 * A327373 A193914 A288490
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 03 2019
STATUS
approved

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Last modified March 28 14:37 EDT 2024. Contains 371254 sequences. (Running on oeis4.)