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.

User: Anna Petrone

Anna Petrone's wiki page.

Anna Petrone has authored 140 sequences. Here are the ten most recent ones:

A245882 Number of distinct Laplacian polynomials among all connected graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 6, 21, 110, 793, 10251, 239307, 10985229
Offset: 1

Views

Author

Travis Hoppe and Anna Petrone, Aug 05 2014

Keywords

Comments

The Laplacian polynomial is the characteristic polynomial of the Laplacian matrix, L = A-D where A is the adjacency matrix and D the degree matrix.

Links

A245883 Number of distinct chromatic polynomials among all connected graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 5, 14, 50, 231, 1650, 21121, 584432
Offset: 1

Views

Author

Travis Hoppe and Anna Petrone, Aug 05 2014

Keywords

Comments

A stable partition of a graph is a set partition of the vertices where no edge has both ends in the same block. The chromatic polynomial is given by chi_G(x) = Sum_p (x)k, where the sum is over all stable partitions of G, k is the length (number of blocks) of p, and (x)_k is the falling factorial x(x-1)(x-2)...(x-k+1). - _Gus Wiseman, Nov 24 2018

Examples

			From _Gus Wiseman_, Nov 24 2018: (Start)
The a(4) = 5 chromatic polynomials:
  -6x + 11x^2 - 6x^3 + x^4
  -4x +  8x^2 - 5x^3 + x^4
  -2x +  5x^2 - 4x^3 + x^4
  -3x +  6x^2 - 4x^3 + x^4
   -x +  3x^2 - 3x^3 + x^4
(End)

Links

Crossrefs

Cf. A229048 (simple graphs, including disconnected ones, with unique chromatic polynomials).
Cf. A001187, A001349, A006125, A125702, A229048, A240936, A245883, A277203, A321911, A322011.

Programs

  • Mathematica
    spsu[,{}]:={{}};spsu[foo,set:{i_,_}]:=Join@@Function[s,Prepend[#,s]&/@spsu[Select[foo,Complement[#,Complement[set,s]]=={}&],Complement[set,s]]]/@Cases[foo,{i,_}];
falling[x_,k_]:=Product[(x-i),{i,0,k-1}];
chromPoly[g_]:=Expand[Sum[falling[x,Length[stn]],{stn,spsu[Select[Subsets[Union@@g],Select[DeleteCases[g,{_}],Function[ed,Complement[ed,#]=={}]]=={}&],Union@@g]}]];
simpleSpans[n_]:=simpleSpans[n]=If[n==0,{{}},Union@@Table[If[#=={},Union[ine,{{n}}],Union[Complement[ine,List/@#],{#,n}&/@#]]&/@Subsets[Range[n-1]],{ine,simpleSpans[n-1]}]];
csm[s_]:=With[{c=Select[Tuples[Range[Length[s]],2],And[OrderedQ[#],UnsameQ@@#,Length[Intersection@@s[[#]]]>0]&]},If[c=={},s,csm[Union[Append[Delete[s,List/@c[[1]]],Union@@s[[c[[1]]]]]]]]];
Table[Length[Union[chromPoly/@Select[simpleSpans[n],Length[csm[#]]==1&]]],{n,5}] (* Gus Wiseman, Nov 24 2018 *)

A245881 Number of distinct Tutte polynomials among all connected graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 5, 16, 73, 532, 7245, 192605, 9717156
Offset: 1

Views

Author

Travis Hoppe and Anna Petrone, Aug 05 2014

Keywords

Links

Crossrefs

Cf. A243049 (simple graphs, including disconnected ones, with unique Tutte polynomials).

Extensions

Terms corrected by Eric M. Schmidt, Mar 20 2015

A245880 Number of distinct characteristic polynomials among all connected graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 6, 21, 111, 821, 10423, 236064, 10375796
Offset: 1

Views

Author

Travis Hoppe and Anna Petrone, Aug 05 2014

Keywords

Links

Crossrefs

Cf. A082104 (simple graphs, including disconnected ones, with unique characteristic polynomials).

Extensions

Terms corrected by Eric M. Schmidt, Mar 20 2015

A245879 Number of distinct fractional chromatic numbers among all connected graphs on n nodes.

Original entry on oeis.org

1, 1, 2, 3, 5, 7, 11, 17, 29, 50
Offset: 1

Views

Author

Travis Hoppe and Anna Petrone, Aug 05 2014

Keywords

Links

Crossrefs

Cf. A243251 (fractional chromatic gap).

A243800 Number of simple connected graphs on n nodes whose maximum size of an independent edge set is equal to 2.

Original entry on oeis.org

0, 0, 0, 5, 20, 16, 22, 29, 37, 46
Offset: 1

Views

Author

Travis Hoppe and Anna Petrone, Jul 15 2014

Keywords

Comments

An independent edge set is a subset of the edges such that no two edges in the subset share a vertex. A maximum independent edge set is an independent edge set containing the largest possible number of edges among all independent edge sets.
The maximum size of an independent edge set is also called the matching number of the graph. - Andrew Howroyd, Sep 05 2019

Links

Crossrefs

Column k=2 of A325304.
Cf. A243801 (max size of independent edge set=3).

A243801 Number of simple connected graphs on n nodes whose maximum size of an independent edge set is equal to 3.

Original entry on oeis.org

0, 0, 0, 0, 0, 95, 830, 790, 1479, 2625
Offset: 1

Views

Author

Travis Hoppe and Anna Petrone, Jul 15 2014

Keywords

Comments

An independent edge set is a subset of the edges such that no two edges in the subset share a vertex. A maximum independent edge set an independent edge set containing the largest possible number of edges among all independent edge sets.
The maximum size of an independent edge set is also called the matching number of the graph. - Andrew Howroyd, Sep 05 2019

Links

Crossrefs

Column k=2 of A325304.
Cf. A243800 (max size of independent edge set=2).

A244427 Number of unlabeled, connected graphs on n vertices with no subgraph isomorphic to a bull-graph.

Original entry on oeis.org

1, 1, 2, 6, 9, 26, 80, 340, 1690, 11432, 101142, 1228608, 20329150
Offset: 1

Views

Author

Travis Hoppe and Anna Petrone, Jun 27 2014

Keywords

Links

Crossrefs

Cf. A079575 (no induced bull subgraph).

Extensions

a(11)-a(13) added using tinygraph by Falk Hüffner, Jul 01 2018

A243799 Number of connected graphs with n nodes that are chordal and are open-bowtie free.

Original entry on oeis.org

1, 1, 2, 5, 6, 13, 25, 58, 130, 316, 769, 1962, 5052, 13342, 35629, 96671
Offset: 1

Views

Author

Travis Hoppe and Anna Petrone, Jun 27 2014

Keywords

Comments

The open bowtie graph is also known as a cricket. - Falk Hüffner, Jul 01 2018

Links

Crossrefs

Cf. A048192 (chordal graphs), A242791 (open-bowtie free graphs).

Extensions

Definition corrected (connected only) by Falk Hüffner, Jul 01 2018
a(11)-a(16) added using tinygraph by Falk Hüffner, Jul 01 2018

A243798 Number of connected graphs with n nodes that are chordal and have no subgraph isomorphic to the bull graph.

Original entry on oeis.org

1, 1, 2, 5, 6, 12, 25, 55, 126, 304, 745, 1893, 4893, 12916, 34562, 93844
Offset: 1

Views

Author

Travis Hoppe and Anna Petrone, Jun 27 2014

Keywords

Links

Crossrefs

Cf. A048192 (chordal graphs), A244427 (no bull subgraphs).

Extensions

Definition corrected (connected only) by Falk Hüffner, Jul 01 2018
a(11)-a(16) added using tinygraph by Falk Hüffner, Jul 01 2018

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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