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 A327336 Number of labeled simple graphs with vertex-connectivity 1. 12
 0, 0, 1, 3, 28, 490, 15336, 851368, 85010976, 15615858960, 5388679220480, 3548130389657216, 4507988483733389568, 11145255551131555572992, 53964198507018134569758720, 514158235191699333805861463040, 9672967865350359173180572164444160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Same as A327114 except a(2) = 1. The vertex-connectivity of a graph is the minimum number of vertices that must be removed (along with any incident edges) to obtain a non-connected graph or singleton. LINKS Andrew Howroyd, Table of n, a(n) for n = 0..50 EXAMPLE The a(2) = 1 through a(4) = 28 edge-sets: {12} {12,13} {12,13,14} {12,23} {12,13,24} {13,23} {12,13,34} {12,14,23} {12,14,34} {12,23,24} {12,23,34} {12,24,34} {13,14,23} {13,14,24} {13,23,24} {13,23,34} {13,24,34} {14,23,24} {14,23,34} {14,24,34} {12,13,14,23} {12,13,14,24} {12,13,14,34} {12,13,23,24} {12,13,23,34} {12,14,23,24} {12,14,24,34} {12,23,24,34} {13,14,23,34} {13,14,24,34} {13,23,24,34} {14,23,24,34} 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]]]]]]]]]; vertConnSys[vts_, eds_]:=Min@@Length/@Select[Subsets[vts], Function[del, Length[del]==Length[vts]-1||csm[DeleteCases[DeleteCases[eds, Alternatives@@del, {2}], {}]]!={Complement[vts, del]}]]; Table[Length[Select[Subsets[Subsets[Range[n], {2}]], vertConnSys[Range[n], #]==1&]], {n, 0, 4}] CROSSREFS Column k = 1 of A327334. The unlabeled version is A052442. Connected non-separable graphs are A013922. Set-systems with vertex-connectivity 1 are A327128. Labeled simple graphs with cut-connectivity 1 are A327114. Cf. A006129, A054592, A322389, A322390, A326786, A327070, A327098, A327100, A327125, A327126. Sequence in context: A346315 A058804 A327114 * A355473 A180710 A005328 Adjacent sequences: A327333 A327334 A327335 * A327337 A327338 A327339 KEYWORD nonn AUTHOR Gus Wiseman, Sep 02 2019 EXTENSIONS Terms a(6) and beyond from Andrew Howroyd, Sep 11 2019 STATUS approved

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Last modified May 31 15:16 EDT 2023. Contains 363068 sequences. (Running on oeis4.)