A185131 -id:A185131 - cp's OEIS frontend

A184951 Irregular triangle C(n,g) counting the connected 5-regular simple graphs on 2n vertices with girth at least g.

1, 3, 60, 1, 7848, 1, 3459383, 7, 2585136675, 388, 2807105250897, 406824

Offset: 3

Jason Kimberley, Jan 10 2012

The first column is for girth at least 3. The row length sequence starts: 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4. The row length is incremented to g-2 when 2n reaches A054760(5,g).

			1;
3;
60, 1;
7848, 1;
3459383, 7;
2585136675, 388;
2807105250897, 406824;

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Connected 5-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A006821 (g=3), A058275 (g=4), A205295 (g=5).
Connected 5-regular simple graphs with girth exactly g: A184950 (triangle); chosen g: A184953 (g=3), A184954 (g=4), A184955 (g=5).
Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth at least g: A185131 (k=3), A184941 (k=4), this sequence (k=5), A184961 (k=6), A184971 (k=7), A184981 (k=8).

a(14) from Jason Kimberley, Dec 26 2012

A184961 Irregular triangle C(n,g) read by rows, counting the connected 6-regular simple graphs on n vertices with girth at least g.

Original entry on oeis.org

1, 1, 4, 21, 266, 7849, 1, 367860, 0, 21609300, 1, 1470293675, 1, 113314233808, 9, 9799685588936, 6

Offset: 7

Jason Kimberley, Jan 10 2012

The first column is for girth at least 3. The row length sequence starts: 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3. The row length is incremented to g-2 when n reaches A054760(6,g).

			Triangle begins:
1;
1;
4;
21;
266;
7849, 1;
367860, 0;
21609300, 1;
1470293675, 1;
113314233808, 9;
9799685588936, 6;

Andries E. Brouwer, Cages
Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Connected 6-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A006822 (g=3), A058276 (g=4).
Connected 6-regular simple graphs with girth exactly g: A184960 (triangle); chosen g: A184963 (g=3), A184964 (g=4).
Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth at least g: A185131 (k=3), A184941 (k=4), A184951 (k=5), this sequence (k=6), A184971 (k=7), A184981 (k=8).

A184971 Irregular triangle C(n,g) counting the connected 7-regular simple graphs on 2n vertices with girth at least g.

Original entry on oeis.org

1, 5, 1547, 21609301, 1, 733351105934, 1

Offset: 4

Jason Kimberley, Jan 10 2012

The first column is for girth at least 3. The row length sequence starts: 1, 1, 1, 2, 2, 2, 2, 2. The row length is incremented to g-2 when 2n reaches A054760(7,g).

			1;
5;
1547;
21609301, 1;
733351105934, 1;
?, 8;
?, 741;
?, 2887493;

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Connected 7-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A014377 (g=3), A181153 (g=4).
Connected 7-regular simple graphs with girth exactly g: A184970 (triangle); chosen g: A184973 (g=3), A184974 (g=4).
Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth at least g: A185131 (k=3), A184941 (k=4), A184951 (k=5), A184961 (k=6), this sequence (k=7), A184981 (k=8).

A184991 Irregular triangle C(n,g) counting the connected 9-regular simple graphs on 2n vertices with girth at least g.

Original entry on oeis.org

1, 9, 88193, 113314233813

Offset: 5

Jason Kimberley, Feb 03 2012

The first column is for girth at least 3. The row length is incremented to g-2 when 2n reaches A054760(9,g).

			1;
 9;
 88193;
 113314233813;
 ?, 1;
 ?, 1;
 ?, 14;

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Connected 9-regular simple graphs with girth at least g: this sequence (triangle); chosen g: A014381 (g=3), A181170 (g=4).
Connected 9-regular simple graphs with girth exactly g: A184990 (triangle); chosen g: A184983 (g=3).
Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth at least g: A185131 (k=3), A184941 (k=4), A184951 (k=5), A184961 (k=6), A184971 (k=7), A184981 (k=8), this sequence (k=9).

A210709 Number of trivalent connected simple graphs with 2n nodes and girth at least 9.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18

Offset: 0

Jason Kimberley, Dec 20 2012

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Trivalent simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8), this sequence (g=9).

Trivalent simple graphs with girth exactly g: A198303 (triangle); chosen g: A006923 (g=3), A006924 (g=4), A006925 (g=5), A006926 (g=6), A006927 (g=7).

a(29) = a(A000066(9)/2) = A052453(9) = 18 is the number of (3,9) cages.

A260811 Number of trivalent bipartite connected simple graphs with 2n nodes and girth at least 6.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 1, 1, 3, 10, 28, 162, 1201, 11415, 125571, 1514489

Offset: 0

Dylan Thurston, Jul 31 2015

The null graph on 0 vertices is vacuously connected, 3-regular, and bipartite; since it is acyclic, it has infinite girth.

G. Brinkmann, Fast generation of cubic graphs, Journal of Graph Theory, 23(2):139-149, 1996.
House of Graphs, Cubic bipartite graphs

Connected 3-regular simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).

Connected bipartite trivalent simple graphs with girth at least g: A006823 (g=4), this sequence (g=6), A260813 (g=8).

A260813 Number of trivalent bipartite connected simple graphs with 2n nodes and girth at least 8.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 3, 10, 101, 2510, 79605, 2607595, 81716416, 2472710752

Offset: 0

Dylan Thurston, Jul 31 2015

The null graph on 0 vertices is vacuously connected, 3-regular, and bipartite; since it is acyclic, it has infinite girth.

G. Brinkmann, Fast generation of cubic graphs, Journal of Graph Theory, 23(2):139-149, 1996.
G. Brinkmann, J. Goedgebeur and B.D. McKay, The Minimality of the Georges-Kelmans Graph, arXiv:2101.00943 [math.CO], 2021.
House of Graphs, Cubic bipartite graphs

Connected 3-regular simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).

Connected bipartite trivalent simple graphs with girth at least g: A006823 (g=4), A260811 (g=6), this sequence (g=8).

a(23)-a(24) from the House-of-Graphs added by R. J. Mathar, Sep 29 2017

a(25)-a(26) from Jan Goedgebeur, Aug 17 2021

cp's OEIS Frontend

A184951 Irregular triangle C(n,g) counting the connected 5-regular simple graphs on 2n vertices with girth at least g.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A184961 Irregular triangle C(n,g) read by rows, counting the connected 6-regular simple graphs on n vertices with girth at least g.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A184971 Irregular triangle C(n,g) counting the connected 7-regular simple graphs on 2n vertices with girth at least g.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A184991 Irregular triangle C(n,g) counting the connected 9-regular simple graphs on 2n vertices with girth at least g.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

A210709 Number of trivalent connected simple graphs with 2n nodes and girth at least 9.

Views

Author

Keywords

Links

Crossrefs

Formula

A260811 Number of trivalent bipartite connected simple graphs with 2n nodes and girth at least 6.

Views

Author

Keywords

Comments

Links

Crossrefs

A260813 Number of trivalent bipartite connected simple graphs with 2n nodes and girth at least 8.

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions