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A014374 Number of trivalent connected simple graphs with 2n nodes and girth at least 6. 20
1, 0, 0, 0, 0, 0, 0, 1, 1, 5, 32, 385, 7574, 181227, 4624501, 122090544, 3328929954, 93990692595, 2754222605376 (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]


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

M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. [Jason Kimberley, Jan 29 2011]


Table of n, a(n) for n=0..18.

House of Graphs, Cubic graphs

Jason Kimberley, Connected regular graphs with girth at least 6

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. [Jason Kimberley, Jan 29 2011]


From Jason Kimberley, May 18 2010 and 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), this sequence (k=3), A058348 (k=4).

Connected 3-regular simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), this sequence (g=6), A014375 (g=7), A014376 (g=8).

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

Sequence in context: A135250 A006926 A185136 * A185336 A125709 A203112

Adjacent sequences:  A014371 A014372 A014373 * A014375 A014376 A014377




N. J. A. Sloane.


Terms a(16) and a(17) appended, from running Meringer's GENREG for 18.6 and 530 processor days at U. Ncle., by Jason Kimberley on May 18 2010

Term a(18) from House of Graphs via Jason Kimberley, May 21 2017



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Last modified April 16 02:35 EDT 2021. Contains 343030 sequences. (Running on oeis4.)