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A058348 Number of connected 4-regular simple graphs on n vertices with girth at least 6. 14
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 4, 0, 19, 0, 1272, 25, 494031, 13504 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,31
COMMENTS
From Jason Kimberley, 2011: (Start)
The null graph on 0 vertices is vacuously connected and 4-regular; since it is acyclic, it has infinite girth.
Does a(2n+1) ever exceed a(2n)?
(End)
LINKS
M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146. [Jason Kimberley, Jan 29 2011]
CROSSREFS
From Jason Kimberley, Jan 29 2011: (Start)
Connected k-regular simple graphs with girth at least 6: A186726 (any k), A186716 (triangle); specified degree k: A185116 (k=2), A014374 (k=3), this sequence (k=4).
Connected 4-regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), A058343 (g=5), this sequence (g=6).
Connected 4-regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), A184945 (g=5). (End)
Sequence in context: A244310 A334705 A156457 * A184946 A351615 A362058
KEYWORD
nonn,more,hard
AUTHOR
N. J. A. Sloane, Dec 17 2000
EXTENSIONS
Jason Kimberley inserted Meringer's computed terms a(n)=0 for n in [27,29,31,33] and appended terms a(35) and a(36), by running Meringer's GENREG for 17 and 106 processor days at U. Ncle, on May 04 2010.
a(37) appended from running GENREG for 450 processor days at U. Ncle. by Jason Kimberley, Dec 03 2011
STATUS
approved

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Last modified February 21 10:54 EST 2024. Contains 370233 sequences. (Running on oeis4.)