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 A058275 Number of connected 5-regular simple graphs on 2n vertices with girth at least 4. 18
 1, 0, 0, 0, 0, 1, 1, 7, 388, 406824, 1125022325, 3813549359274 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,8 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] 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] LINKS Jason Kimberley, Connected regular graphs with girth at least 4 M. Meringer, Tables of Regular Graphs FORMULA a(n) = A185354(n) - A185254(n); This sequence is the inverse Euler transformation of A185354. - Jason Kimberley, Nov 04 2011. 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: A299036 A112905 A293459 * A184954 A185354 A222893 Adjacent sequences:  A058272 A058273 A058274 * A058276 A058277 A058278 KEYWORD nonn,more,hard AUTHOR N. J. A. Sloane, Dec 17 2000 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. STATUS approved

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)