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 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. 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

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