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A014371 Number of trivalent connected simple graphs with 2n nodes and girth at least 4. 27
1, 0, 0, 1, 2, 6, 22, 110, 792, 7805, 97546, 1435720, 23780814, 432757568, 8542471494, 181492137812, 4127077143862 (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. [From Jason Kimberley, Jan 29 2011]


G. Brinkmann, J. Goedgebeur and B.D. McKay, Generation of Cubic graphs, Discrete Mathematics and Theoretical Computer Science, 13 (2) (2011), 69-80.

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.


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

House of Graphs, Cubic graphs.

Jason Kimberley, Connected regular graphs with girth at least 4

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

M. Meringer, Tables of Regular Graphs.


Contribution from Jason Kimberley, Jun 28 2010 and Jan 29 2011: (Start)

3-regular simple graphs with girth at least 4: this sequence (connected), A185234 (disconnected), A185334 (not necessarily connected).

Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: A185114 (k=2), this sequence (k=3), A033886 (k=4), A058275 (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).

Connected 3-regular simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), this sequence (g=4), A014372 (g=5), A014374 (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: A129535 A216720 A290279 * A111280 A095817 A101042

Adjacent sequences:  A014368 A014369 A014370 * A014372 A014373 A014374




N. J. A. Sloane.


Terms a(14) and a(15) appended, from running Meringer's GENREG for 4.2 and 93.2 processor days at U. Newcastle, by Jason Kimberley on Jun 28 2010.

a(16), from House of Graphs, by Jan Goedgebeur et al. [From Jason Kimberley, Feb 15 2011]



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Last modified March 25 15:02 EDT 2019. Contains 321470 sequences. (Running on oeis4.)