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A014372 Number of trivalent connected simple graphs with 2n nodes and girth at least 5. 21
1, 0, 0, 0, 0, 1, 2, 9, 49, 455, 5783, 90938, 1620479, 31478584, 656783890, 14621871204, 345975648562 (list; graph; refs; listen; history; text; internal format)



The null graph on 0 vertices is vacuously connected and 3-regular; since it is acyclic, it has infinite girth. - Jason Kimberley, Jan 29 2011

Brendan McKay has observed that a(13) = 31478584 is output by genreg, minibaum, and snarkhunter, but Meringer's table currently has a(13) = 31478582. - Jason Kimberley, May 17 2017


CRC Handbook of Combinatorial Designs, 1996, p. 647.


Table of n, a(n) for n=0..16.

G. Brinkmann, J. Goedgebeur and B. D. McKay, Generation of cubic graphs, Discr. Math. Theor. Comp. Sci. 13 (2) (2011) 69-80.

House of Graphs, Cubic graphs.

Jason Kimberley, Connected regular graphs with girth at least 5

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

M. Meringer, Tables of Regular Graphs

M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146.


Contribution from Jason Kimberley, 2010, 2011, and 2012: (Start)

3-regular simple graphs with girth at least 5: this sequence (connected), A185235 (disconnected), A185335 (not necessarily connected).

Connected k-regular simple graphs with girth at least 5: A186725 (all k), A186715 (triangle); A185115 (k=2), this sequence (k=3), A058343 (k=4), A205295 (g=5).

Connected 3-regular simple graphs with girth at least g: A185131 (triangle); A002851 (g=3), A014371 (g=4), this sequence (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).

Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); A006923 (g=3), A006924 (g=4), A006925 (g=5), A006926 (g=6), A006927 (g=7). (End)

Sequence in context: A000167 A241785 A109323 * A185335 A262752 A138416

Adjacent sequences:  A014369 A014370 A014371 * A014373 A014374 A014375




N. J. A. Sloane.


Terms a(15) and a(16) appended, from running Meringer's GENREG for 28.7 and 715.2 processor days at U. Ncle., by Jason Kimberley, Jun 28 2010.



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Last modified April 16 03:25 EDT 2021. Contains 343030 sequences. (Running on oeis4.)