A123537
Erroneous version of A005644 (there appears to be a typo in a(9)).
Original entry on oeis.org
1, 26, 1768, 225096, 51725352, 21132802554, 15463799747936, 20604021770403328, 50928019401158515328, 237644423948928994197504, 2125373296900166452199861760
Offset: 4
- Walsh, T. R. S.; Counting labeled three-connected and homeomorphically irreducible two-connected graphs. J. Combin. Theory Ser. B 32 (1982), no. 1, 1-11.
A327198
Number of labeled simple graphs covering n vertices with vertex-connectivity 2.
Original entry on oeis.org
0, 0, 0, 1, 9, 212, 9600, 789792, 114812264, 29547629568, 13644009626400, 11489505388892800, 17918588321874717312, 52482523149603539181312, 292311315623259148521270784, 3129388799344153886272170009600, 64965507855114369076680860799267840
Offset: 0
Cf.
A005644,
A013922,
A052442,
A259862,
A326786,
A327082,
A327101,
A327112,
A327113,
A327126,
A327227.
-
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],#]==2&]],{n,0,5}]
A123542
Triangular array T(n,k) giving number of 3-connected graphs with n labeled nodes and k edges (n >= 4, ceiling(3*n/2) <= k <= n(n-1)/2).
Original entry on oeis.org
1, 15, 10, 1, 70, 492, 690, 395, 105, 15, 1, 5040, 28595, 58905, 63990, 42392, 18732, 5880, 1330, 210, 21, 1, 16800, 442680, 2485920, 6629056, 10684723, 11716068, 9409806, 5824980, 2872317, 1147576, 373156, 98112, 20475, 3276
Offset: 4
Triangle begins:
n = 4
k = 6 : 1
Total( 4) = 1
n = 5
k = 8 : 15
k = 9 : 10
k = 10 : 1
Total( 5) = 26
n = 6
k = 9 : 70
k = 10 : 492
k = 11 : 690
k = 12 : 395
k = 13 : 105
k = 14 : 15
k = 15 : 1
Total( 6) = 1768
n = 7
k = 11 : 5040
k = 12 : 28595
k = 13 : 58905
k = 14 : 63990
k = 15 : 42392
k = 16 : 18732
k = 17 : 5880
k = 18 : 1330
k = 19 : 210
k = 20 : 21
k = 21 : 1
Total( 7) = 225096
- R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977.
A338414
Number of labeled 3-connected graphs with n edges.
Original entry on oeis.org
1, 0, 15, 80, 493, 5730, 45790, 501690, 5747805, 66738169, 884847355, 12032825028, 174686734180, 2698980641742, 43470161714616, 739558796434277, 13161203468888236, 244555222834161480
Offset: 6
Showing 1-4 of 4 results.
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