login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A186729 Number of connected regular simple graphs on n vertices with girth at least 9. 10
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 (list; graph; refs; listen; history; text; internal format)
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 * A226373 A240952 A221749

Adjacent sequences:  A186726 A186727 A186728 * A186730 A186731 A186732

KEYWORD

nonn,hard,more

AUTHOR

Jason Kimberley, Oct 22 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 6 04:14 EST 2019. Contains 329784 sequences. (Running on oeis4.)