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A014382
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Number of connected regular graphs of degree 10 with n nodes.
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13
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 10, 540, 805579, 2585136741, 9799685588961, 42700033549946255, 214755319657939505396, 1251392240942040452186675, 8462215143144463851848329660, 66398444413512642732641312352087, 603696608755863722277922645973602843, 6346188247029220928621633703157327186101
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OFFSET
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0,14
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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EXAMPLE
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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
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CROSSREFS
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10-regular simple graphs: this sequence (connected), A185203 (disconnected).
Connected regular simple graphs 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), this sequence (k=10), A014384 (k=11).
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KEYWORD
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nonn,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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