A014374 Number of trivalent connected simple graphs with 2n nodes and girth at least 6.

1, 0, 0, 0, 0, 0, 0, 1, 1, 5, 32, 385, 7574, 181227, 4624501, 122090544, 3328929954, 93990692595, 2754222605376

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• more
• hard

Comments

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]

References

• 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]

Links

• 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]

Crossrefs

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)

Extensions

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