A014376 Number of trivalent connected simple graphs with 2n nodes and girth at least 8.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 3, 13, 155, 4337, 266362, 20807688

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• more
• hard

References

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

Links

• Jason Kimberley, Connected regular graphs with girth at least 8
• 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, Journal of Graph Theory, 30 (1999), 137-146.

Crossrefs

Contribution from Jason Kimberley, May 18 2010 and Jan 29 2011: (Start)

Connected k-regular simple graphs with girth at least 8: A186728 (any k), A186718 (triangle); specific k: A185118 (k=2), this sequence (k=3).

Trivalent simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), this sequence (g=8).

Trivalent 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(21), a(22), and a(23) found by running Meringer's GENREG for 0.15, 5.0, and 176.2 processor days, respectively, at U. Ncle. by Jason Kimberley, May 18 2010