OFFSET
0,14
COMMENTS
Since the nontrivial 10-regular graph with the least number of vertices is K_11, there are no disconnected 10-regular graphs with less than 22 vertices. Thus for n<22 this sequence also gives the number of all 10-regular graphs on n vertices. - Jason Kimberley, Sep 25 2009
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.
LINKS
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.
Eric Weisstein's World of Mathematics, Regular Graph.
EXAMPLE
The null graph on 0 vertices is vacuously connected and 10-regular; since it is acyclic, it has infinite girth. - Jason Kimberley, Feb 10 2011
CROSSREFS
10-regular simple graphs: this sequence (connected), A185203 (disconnected).
KEYWORD
nonn,hard
AUTHOR
EXTENSIONS
Using the symmetry of A051031, a(16) and a(17) from Jason Kimberley, Sep 25 2009 and Jan 03 2011
a(18)-a(21) from Andrew Howroyd, Mar 13 2020
a(22)-a(24) from Andrew Howroyd, May 19 2020
STATUS
approved