A186716 Irregular triangle C(n,k): the number of connected k-regular graphs on n vertices having girth at least six.

1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 5, 0, 0, 1, 0, 0, 0, 1, 32, 0, 0, 1, 0, 0, 0, 1, 385, 0, 0, 1, 0, 0, 0, 1, 7574, 0, 0, 1, 0, 0, 0, 1, 181227, 1, 0, 0, 1, 0, 0, 0, 0, 1

Offset

1,53

Comments

Other than the first two rows, each row begins with 0, 0, 1.

References

M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146.

Links

Jason Kimberley, Rows n = 1..37 of triangle, flattened

House of Graphs, Cubic graphs

Jason Kimberley, Connected regular graphs with girth at least 6

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

M. Meringer, Tables of Regular Graphs

M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146.

Example

1;
0, 1;
0, 0;
0, 0;
0, 0;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1;
0, 0, 1, 1;
0, 0, 1, 0;
0, 0, 1, 1;
0, 0, 1, 0;
0, 0, 1, 5;
0, 0, 1, 0;
0, 0, 1, 32;
0, 0, 1, 0;
0, 0, 1, 385;
0, 0, 1, 0;
0, 0, 1, 7574;
0, 0, 1, 0;
0, 0, 1, 181227, 1;
0, 0, 1, 0, 0;
0, 0, 1, 4624501, 1;
0, 0, 1, 0, 0;
0, 0, 1, 122090544, 4;
0, 0, 1, 0, 0;
0, 0, 1, 3328929954, 19;
0, 0, 1, 0, 0;
0, 0, 1, 93990692595, 1272;
0, 0, 1, 0, 25;
0, 0, 1, 2754222605376, 494031;
0, 0, 1, 0, 13504;

Crossrefs

Connected k-regular simple graphs with girth at least 6: A186726 (any k), this sequence (triangle); specific k: A185116 (k=2), A014374 (k=3), A058348 (k=4).

Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth at least g: A068934 (g=3), A186714 (g=4), A186715 (g=5), this sequence (g=6), A186717 (g=7), A186718 (g=8), A186719 (g=9).

Triangular arrays C(n,k) counting connected simple k-regular graphs on n vertices with girth exactly g: A186733 (g=3), A186734 (g=4).

Sequence in context: A294393 A047754 A048682 * A331039 A171915 A287703

Adjacent sequences: A186713 A186714 A186715 * A186717 A186718 A186719

Keyword

nonn,hard,tabf

Author

Jason Kimberley, Nov 23 2011

Extensions

C(36,3) from House of Graphs via Jason Kimberley, May 21 2017

Status

approved