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A058275
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Number of connected 5-regular simple graphs on 2n vertices with girth at least 4.
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18
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1, 0, 0, 0, 0, 1, 1, 7, 388, 406824, 1125022325, 3813549359274
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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COMMENTS
| The null graph on 0 vertices is vacuously connected and 5-regular; since it is acyclic, it has infinite girth. [From Jason Kimberley, Jan 30 2011]
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REFERENCES
| M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. [From Jason Kimberley, Jan 30 2011]
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LINKS
| Jason Kimberley, Connected regular graphs with girth at least 4
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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FORMULA
| a(n) = A185354(n) - A185254(n);
This sequence is the inverse Euler transformation of A185354. - Jason Kimberley, Nov 04 2011.
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CROSSREFS
| Contribution from Jason Kimberley, Jan 30 and Nov 04 2011: (Start)
5-regular simple graphs on 2n vertices with girth at least 4: this sequence (connected), A185254 (disconnected), A185354 (not necessarily connected).
Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: A185114 (k=2), A014371 (k=3), A033886 (k=4), this sequence (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).
Connected 5-regular simple graphs with girth at least g: A006821 (g=3), this sequence (g=4), A205295 (g=5).
Connected 5-regular simple graphs with girth exactly g: A184953 (g=3), A184954 (g=4), A184955 (g=5). (End)
Sequence in context: A140638 A112905 * A184954 A185354 A009712 A128793
Adjacent sequences: A058272 A058273 A058274 * A058276 A058277 A058278
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KEYWORD
| nonn,more,hard,changed
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 17 2000
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EXTENSIONS
| Terms a(10) and a(11) appended, from running Meringer's GENREG for 3.8 and 7886 processor days at U. Ncle., by Jason Kimberley on Jun 28 2010.
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