

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 kregular simple graphs with girth at least g


EXAMPLE

The null graph is vacuously regular; there is one 0regular simple graph with 1 vertex, and one 1regular simple graph with 2 vertices; each of those three graphs, being acyclic, has infinite girth.
The ncycle is the connected 2regular 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 kregular 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



