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A327147 Smallest BII-number of a set-system with spanning edge-connectivity n. 4
0, 1, 52, 116, 3952, 8052 (list; graph; refs; listen; history; text; internal format)



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.

The spanning edge-connectivity of a set-system is the minimum number of edges that must be removed (without removing incident vertices) to obtain a set-system that is disconnected or covers fewer vertices.


Table of n, a(n) for n=0..5.


The sequence of terms together with their corresponding set-systems begins:

     0: {}

     1: {{1}}

    52: {{1,2},{1,3},{2,3}}

   116: {{1,2},{1,3},{2,3},{1,2,3}}

  3952: {{1,3},{2,3},{1,4},{2,4},{3,4},{1,2,3},{1,2,4}}

  8052: {{1,2},{1,3},{2,3},{1,4},{2,4},{3,4},{1,2,3},{1,2,4},{1,3,4}}


The same for cut-connectivity is A327234.

The same for non-spanning edge-connectivity is A002450.

The spanning edge-connectivity of the set-system with BII-number n is A327144(n).

Cf. A000120, A048793, A070939, A323818, A326031, A326786, A326787, A327041, A327069, A327076, A327108, A327111, A327130, A327145.

Sequence in context: A044620 A209988 A326912 * A120534 A122166 A205221

Adjacent sequences:  A327144 A327145 A327146 * A327148 A327149 A327150




Gus Wiseman, Sep 01 2019



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Last modified February 24 18:32 EST 2021. Contains 341577 sequences. (Running on oeis4.)