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A014374
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Number of trivalent connected simple graphs with 2n nodes and girth at least 6.
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18
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1, 0, 0, 0, 0, 0, 0, 1, 1, 5, 32, 385, 7574, 181227, 4624501, 122090544, 3328929954, 93990692595
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refs;
listen;
history;
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internal format)
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OFFSET
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0,10
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COMMENTS
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The null graph on 0 vertices is vacuously connected and 3-regular; since it is acyclic, it has infinite girth. [From Jason Kimberley, Jan 29 2011]
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REFERENCES
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CRC Handbook of Combinatorial Designs, 1996, p. 647.
M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. [From Jason Kimberley, Jan 29 2011]
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LINKS
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Table of n, a(n) for n=0..17.
Jason Kimberley, Connected regular graphs with girth at least 6
Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g
M. Meringer, Tables of Regular Graphs
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CROSSREFS
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Contribution from Jason Kimberley, May 18 2010 and Jan 29 2011: (Start)
Connected k-regular simple graphs with girth at least 6: A186726 (any k), A186716 (triangle); specified degree k: A185116 (k=2), this sequence (k=3), A058348 (k=4).
Connected 3-regular simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), this sequence (g=6), A014375 (g=7), A014376 (g=8).
Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); chosen g: A006923 (g=3), A006924 (g=4), A006925 (g=5), A006926 (g=6), A006927 (g=7). (End)
Sequence in context: A135250 A006926 A185136 * A185336 A125709 A203112
Adjacent sequences: A014371 A014372 A014373 * A014375 A014376 A014377
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KEYWORD
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nonn,more,hard
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Terms a(16) and a(17) appended, from running Meringer's GENREG for 18.6 and 530 processor days at U. Ncle., by Jason Kimberley on May 18 2010.
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STATUS
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approved
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