

A058343


Number of connected 4regular simple graphs on n vertices with girth at least 5.


14



1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 8, 131, 3917, 123859, 4131991, 132160608, 4018022149, 118369811960
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OFFSET

0,21


COMMENTS

The null graph on 0 vertices is vacuously connected and 4regular; since it is acyclic, it has infinite girth. [From Jason Kimberley, Jan 29 2011]


REFERENCES

M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137146. [From Jason Kimberley, Jan 29 2011]


LINKS

Table of n, a(n) for n=0..28.
Jason Kimberley, Connected regular graphs with girth at least 5
Jason Kimberley, Index of sequences counting connected kregular simple graphs with girth at least g
M. Meringer, Tables of Regular Graphs


CROSSREFS

Contribution from Jason Kimberley, 2010, 2011, and 2012: (Start)
4regular simple graphs with girth at least 5: this sequence (connected), A185245 (disconnected), A185345 (not necessarily connected).
Connected kregular simple graphs with girth at least 5: A186725 (all k), A186715 (triangle); A185115 (k=2), A014372 (k=3), this sequence (k=4), A205295 (k=5).
Connected 4regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), this sequence (g=5), A058348 (g=6).
Connected 4regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), A184945 (g=5). (End)
Sequence in context: A178173 A058891 A184945 * A111827 A045330 A193203
Adjacent sequences: A058340 A058341 A058342 * A058344 A058345 A058346


KEYWORD

nonn,more,hard


AUTHOR

N. J. A. Sloane, Dec 17 2000


EXTENSIONS

Terms a(27) and a(28) were appended by Jason Kimberley, from running Meringer's GENREG for 58 and 1563 processor days at U. Ncle, on Mar 19 and Jun 28 2010.


STATUS

approved



