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.

Showing 1-4 of 4 results.

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

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Author

Keywords

References

  • 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

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Author

Gus Wiseman, Sep 01 2019

Keywords

Comments

The vertex-connectivity of a set-system is the minimum number of vertices that must be removed (along with any resulting empty edges) to obtain a non-connected set-system or singleton. Note that this means a single node has vertex-connectivity 0.

Crossrefs

Programs

  • 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],#]==2&]],{n,0,5}]

Formula

a(n) = A013922(n) - A005644(n) for n >= 3. - Andrew Howroyd, Dec 26 2020

Extensions

Terms a(6) and beyond from Andrew Howroyd, Dec 26 2020

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

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Author

N. J. A. Sloane, Nov 13 2006

Keywords

Examples

			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
		

References

  • R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1977.

Crossrefs

Row sums give A005644. Cf. A123527, A123534.

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

Views

Author

Andrew Howroyd, Nov 07 2020

Keywords

Comments

The initial terms of this sequence were computed from A123542.
The smallest 3-connected graph is the complete graph on 4 vertices which has 6 edges.

Crossrefs

Showing 1-4 of 4 results.