

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



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 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)


KEYWORD

nonn,more,hard


AUTHOR



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



