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.

A327146 Number of labeled simple graphs with n vertices and spanning edge-connectivity 2.

This page as a plain text file.
%I A327146 #5 Sep 01 2019 08:39:54
%S A327146 0,0,0,1,9,227
%N A327146 Number of labeled simple graphs with n vertices and spanning edge-connectivity 2.
%C A327146 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.
%H A327146 Gus Wiseman, <a href="/A327146/a327146.png">The a(4) = 9 simple graphs with spanning edge-connectivity 2.</a>
%t A327146 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 A327146 spanEdgeConn[vts_,eds_]:=Length[eds]-Max@@Length/@Select[Subsets[eds],Union@@#!=vts||Length[csm[#]]!=1&];
%t A327146 Table[Length[Select[Subsets[Subsets[Range[n],{2}]],spanEdgeConn[Range[n],#]==2&]],{n,0,4}]
%Y A327146 Column k = 2 of A327069.
%Y A327146 BII-numbers of set-systems with spanning edge-connectivity 2 are A327108.
%Y A327146 The generalization to set-systems is A327130.
%Y A327146 Cf. A006129, A327070, A327071, A327102, A327109, A327111, A327129, A327144.
%K A327146 nonn,more
%O A327146 0,5
%A A327146 _Gus Wiseman_, Aug 27 2019