A186728 Number of connected regular graphs with n nodes and girth at least 8.

1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 14, 1, 156, 1, 4338, 1, 266363, 1, 20807689, 1

Offset: 0

Author

Jason Kimberley, Nov 25 2011

Keywords

• nonn
• hard
• more

References

• M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146.

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

Crossrefs

Connected regular graphs of any degree with girth at least g: A005177 (g=3), A186724 (g=4), A186725 (g=5), A186726 (g=6), A186727 (g=7), this sequence (g=8), A186729 (g=9).

Connected k-regular simple graphs with girth at least 8: this sequence (any k), A186718 (triangle); specific k: A185118 (k=2), A014376 (k=3).

Formula

a(n) = sum of the n-th row of A186718.