OFFSET
0,5
REFERENCES
CRC Handbook of Combinatorial Designs, 1996, p. 648.
I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 131-135 of Problèmes combinatoires et théorie des graphes (Orsay, 9-13 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, Centre Nat. Recherche Scient., Paris, 1978.
R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g
Denis S. Krotov, [[2,10],[6,6]]-equitable partitions of the 12-cube, arXiv:2012.00038 [math.CO], 2020.
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, Nov 24 2009]
Eric Weisstein's World of Mathematics, Quintic Graph
Eric Weisstein's World of Mathematics, Regular Graph
FORMULA
EXAMPLE
a(0)=1 because the null graph (with no vertices) is vacuously 5-regular and connected.
CROSSREFS
Contribution (almost all) from Jason Kimberley, Feb 10 2011: (Start)
5-regular simple graphs: this sequence (connected), A165655 (disconnected), A165626 (not necessarily connected).
Connected regular simple graphs A005177 (any degree), A068934 (triangular array), specified degree k: A002851 (k=3), A006820 (k=4), this sequence (k=5), A006822 (k=6), A014377 (k=7), A014378 (k=8), A014381 (k=9), A014382 (k=10), A014384 (k=11).
Connected 5-regular simple graphs with girth at least g: this sequence (g=3), A058275 (g=4), A205295 (g=5).
Connected 5-regular simple graphs with girth exactly g: A184953 (g=3), A184954 (g=4), A184955 (g=5).
KEYWORD
nonn,nice,hard,more
AUTHOR
EXTENSIONS
By running M. Meringer's GENREG for about 2 processor years at U. Newcastle, a(9) was found by Jason Kimberley, Nov 24 2009
a(10)-a(14) from Andrew Howroyd, Mar 10 2020
STATUS
approved