cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A327069 Triangle read by rows where T(n,k) is the number of labeled simple graphs with n vertices and spanning edge-connectivity k.

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%I A327069 #14 May 26 2021 02:14:33
%S A327069 1,1,0,1,1,0,4,3,1,0,26,28,9,1,0,296,475,227,25,1,0,6064,14736,10110,
%T A327069 1782,75,1,0
%N A327069 Triangle read by rows where T(n,k) is the number of labeled simple graphs with n vertices and spanning edge-connectivity k.
%C A327069 The spanning edge-connectivity of a graph is the minimum number of edges that must be removed (without removing incident vertices) to obtain a disconnected or empty graph.
%C A327069 We consider a graph with one vertex and no edges to be disconnected.
%e A327069 Triangle begins:
%e A327069     1
%e A327069     1   0
%e A327069     1   1   0
%e A327069     4   3   1   0
%e A327069    26  28   9   1   0
%e A327069   296 475 227  25   1   0
%t A327069 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]]]]]]]]];
%t A327069 spanEdgeConn[vts_,eds_]:=Length[eds]-Max@@Length/@Select[Subsets[eds],Union@@#!=vts||Length[csm[#]]!=1&];
%t A327069 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],spanEdgeConn[Range[n],#]==k&]],{n,0,5},{k,0,n}]
%Y A327069 Row sums are A006125.
%Y A327069 Column k = 0 is A054592, if we assume A054592(1) = 1.
%Y A327069 Column k = 1 is A327071.
%Y A327069 Column k = 2 is A327146.
%Y A327069 The unlabeled version (except with offset 1) is A263296.
%Y A327069 Cf. A001187, A095983, A259862, A322338, A326787, A327070, A327072, A327073.
%K A327069 nonn,tabl,more
%O A327069 0,7
%A A327069 _Gus Wiseman_, Aug 23 2019
%E A327069 a(21)-a(27) from _Robert Price_, May 25 2021