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A014384
Number of connected regular graphs of degree 11 with 2n nodes.
13
1, 0, 0, 0, 0, 0, 1, 13, 8037796, 945095823831333, 187549729101764460261505, 66398444413512642732641312352088, 43100445012087185112567117500931916869587
OFFSET
0,8
COMMENTS
Since the nontrivial 11-regular graph with the least number of vertices is K_12, there are no disconnected 11-regular graphs with less than 24 vertices. Thus for n<24 this sequence also gives the number of all 11-regular graphs on 2n 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.
EXAMPLE
The null graph on 0 vertices is vacuously connected and 11-regular; since it is acyclic, it has infinite girth. - Jason Kimberley, Feb 10 2011
CROSSREFS
11-regular simple graphs: this sequence (connected), A185213 (disconnected).
Connected regular simple graphs (with girth at least 3): A005177 (any degree), A068934 (triangular array), specified degree k: A002851 (k=3), A006820 (k=4), A006821 (k=5), A006822 (k=6), A014377 (k=7), A014378 (k=8), A014381 (k=9), A014382 (k=10), this sequence (k=11).
Sequence in context: A055313 A128669 A013866 * A185213 A034248 A324270
KEYWORD
nonn,hard,more
EXTENSIONS
a(9)-a(10) from Andrew Howroyd, Mar 13 2020
a(11)-a(12) from Andrew Howroyd, May 19 2020
STATUS
approved