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 A181170 Number of connected 9-regular simple graphs on 2n vertices with girth at least 4. 12
 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 14 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 COMMENTS a(11)=14 was computed by the author using GENREG at U. Ncle. over 615 processor days during Dec 2009. LINKS Jason Kimberley, Connected regular graphs with girth at least 4 M. Meringer, Tables of Regular Graphs M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146. EXAMPLE The a(0)=1 null graph is vacuously 8-regular and connected; since it is acyclic then it has infinite girth. The a(9)=1 graph is the complete bipartite graph K_{9,9} with 18 vertices. The a(10)=1 graph has girth 4, automorphism group of order 7257600, and the following adjacency lists: 01 : 02 03 04 05 06 07 08 09 10 02 : 01 11 12 13 14 15 16 17 18 03 : 01 11 12 13 14 15 16 17 19 04 : 01 11 12 13 14 15 16 18 19 05 : 01 11 12 13 14 15 17 18 19 06 : 01 11 12 13 14 16 17 18 19 07 : 01 11 12 13 15 16 17 18 19 08 : 01 11 12 14 15 16 17 18 19 09 : 01 11 13 14 15 16 17 18 19 10 : 01 12 13 14 15 16 17 18 19 11 : 02 03 04 05 06 07 08 09 20 12 : 02 03 04 05 06 07 08 10 20 13 : 02 03 04 05 06 07 09 10 20 14 : 02 03 04 05 06 08 09 10 20 15 : 02 03 04 05 07 08 09 10 20 16 : 02 03 04 06 07 08 09 10 20 17 : 02 03 05 06 07 08 09 10 20 18 : 02 04 05 06 07 08 09 10 20 19 : 03 04 05 06 07 08 09 10 20 20 : 11 12 13 14 15 16 17 18 19 CROSSREFS 9-regular simple graphs with girth at least 4: this sequence (connected), A185294 (disconnected). 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), A058275 (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), this sequence (k=9). Connected 9-regular simple graphs with girth at least g: A014378 (g=3), this sequence (g=4). Connected 9-regular simple graphs with girth exactly g: A184993 (g=3). Sequence in context: A228033 A102910 A262298 * A243830 A002337 A008423 Adjacent sequences:  A181167 A181168 A181169 * A181171 A181172 A181173 KEYWORD nonn,more,hard AUTHOR Jason Kimberley, last week of Jan 2011 STATUS approved

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Last modified July 30 21:33 EDT 2021. Contains 346365 sequences. (Running on oeis4.)