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A165627 Number of 6-regular graphs (sextic graphs) on n vertices. 12
1, 0, 0, 0, 0, 0, 0, 1, 1, 4, 21, 266, 7849, 367860, 21609301, 1470293676, 113314233813, 9799685588961 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,10

COMMENTS

Because the triangle A051031 is symmetric, a(n) is also the number of (n-7)-regular graphs on n vertices.

REFERENCES

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

LINKS

Table of n, a(n) for n=0..17.

Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g

M. Meringer, Tables of Regular Graphs

N. J. A. Sloane, Transforms

FORMULA

Euler transformation of A006822.

CROSSREFS

6-regular simple graphs: A006822 (connected), A165656 (disconnected), this sequence (not necessarily connected).

Regular graphs A005176 (any degree), A051031 (triangular array), chosen degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), A005638 (k=3), A033301 (k=4), A165626 (k=5), this sequence (k=6), A165628 (k=7), A180260 (k=8).

Sequence in context: A185163 A184961 A006822 * A198050 A126458 A048164

Adjacent sequences:  A165624 A165625 A165626 * A165628 A165629 A165630

KEYWORD

nonn,hard,more

AUTHOR

Jason Kimberley, Sep 22 2009

EXTENSIONS

Cross-references edited by the author, Nov 07 2009 and Oct 17 2011.

The author appended a(17) on Dec 30 2010.

STATUS

approved

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Last modified April 18 18:46 EDT 2014. Contains 240732 sequences.