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A014381
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Number of connected regular graphs of degree 9 with 2n nodes.
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15
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1, 0, 0, 0, 0, 1, 9, 88193, 113314233813, 281341168330848874, 1251392240942040452186674, 9854603833337765095207342173991, 134283276101750327256393048776114352985
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OFFSET
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0,7
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COMMENTS
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Since the nontrivial 9-regular graph with the least number of vertices is K_10, there are no disconnected 9-regular graphs with less than 20 vertices. Thus for n<20 this sequence also gives the number of all 9-regular graphs on 2n 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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FORMULA
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EXAMPLE
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The null graph on 0 vertices is vacuously connected and 9-regular; since it is acyclic, it has infinite girth. - Jason Kimberley, Feb 10 2011
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CROSSREFS
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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), this sequence (k=9), A014382 (k=10), A014384 (k=11).
9-regular simple graphs: this sequence (connected), A185293 (disconnected).
Connected 9-regular simple graphs with girth at least g: this sequence (g=3), A181170 (g=4).
Connected 9-regular simple graphs with girth exactly g: A184993 (g=3).
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KEYWORD
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nonn,more,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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