A186729 Number of connected regular simple graphs on n vertices with girth at least 9.

1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 19

Offset

0,59

Links

Table of n, a(n) for n=0..58.

Andries E. Brouwer, Cages

House of Graphs, Cubic graphs

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

Example

The null graph is vacuously regular; there is one 0-regular simple graph with 1 vertex, and one 1-regular simple graph with 2 vertices;  each of those three graphs, being acyclic, has infinite girth.
The n-cycle is the connected 2-regular graph with girth n.
The (3,9)-cages have order 58 and there are 18 of them.

Crossrefs

Connected regular graphs of any degree with girth at least g: A005177 (g=3), A186724 (g=4), A186725 (g=5), A186726 (g=6), A186727 (g=7), A186728 (g=8), this sequence (g=9).

Connected k-regular simple graphs with girth at least 9: this sequence (all k), A186719 (triangular array), A185119 (k=2).

Sequence in context: A013886 A259327 A271975 * A340650 A226373 A240952

Adjacent sequences: A186726 A186727 A186728 * A186730 A186731 A186732

Keyword

nonn,hard,more

Author

Jason Kimberley, Oct 22 2011

Status

approved