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A058343
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Number of connected 4-regular simple graphs on n vertices with girth at least 5.
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14
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1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 8, 131, 3917, 123859, 4131991, 132160608, 4018022149, 118369811960
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,21
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COMMENTS
| The null graph on 0 vertices is vacuously connected and 4-regular; since it is acyclic, it has infinite girth. [From Jason Kimberley, Jan 29 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 29 2011]
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LINKS
| Jason Kimberley, Connected regular graphs with girth at least 5
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
| Contribution from Jason Kimberley, 2010, 2011, and 2012: (Start)
4-regular simple graphs with girth at least 5: this sequence (connected), A185245 (disconnected), A185345 (not necessarily connected).
Connected k-regular simple graphs with girth at least 5: A186725 (all k), A186715 (triangle); A185115 (k=2), A014372 (k=3), this sequence (k=4), A205295 (k=5).
Connected 4-regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), this sequence (g=5), A058348 (g=6).
Connected 4-regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), A184945 (g=5). (End)
Sequence in context: A178173 A058891 A184945 * A111827 A045330 A193203
Adjacent sequences: A058340 A058341 A058342 * A058344 A058345 A058346
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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(27) and a(28) were appended by Jason Kimberley, from running Meringer's GENREG for 58 and 1563 processor days at U. Ncle, on Mar 19 and Jun 28 2010.
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