A184944
Number of connected 4-regular simple graphs on n vertices with girth exactly 4.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 12, 31, 220, 1606, 16828, 193900, 2452818, 32670329, 456028472, 6636066091, 100135577616, 1582718909051
Offset: 0
a(0)=0 because even though the null graph (on zero vertices) is vacuously 4-regular and connected, since it is acyclic, it has infinite girth.
The a(8)=1 graph is the complete bipartite graph K_{4,4}.
4-regular simple graphs with girth exactly 4: this sequence (connected),
A185044 (disconnected),
A185144 (not necessarily connected).
Connected 4-regular simple graphs with girth exactly g:
A184943 (g=3), this sequence (g=4),
A184945 (g=5).
a(23) was appended by the author once
A033886(23) was known, Nov 03 2011
A006926
Number of connected trivalent graphs with 2n nodes and girth exactly 6.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 32, 385, 7573, 181224, 4624480, 122089998, 3328899586, 93988909755
Offset: 0
- CRC Handbook of Combinatorial Designs, 1996, p. 647.
- Gordon Royle, personal communication.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Definition corrected to include "connected", and "girth at least 6" minus "girth at least 7" formula provided by
Jason Kimberley, Dec 12 2009
A006927
Number of connected trivalent graphs with 2n nodes and girth exactly 7.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 21, 545, 30368, 1782839, 95079080, 4686063107
Offset: 0
- Gordon Royle, personal communication.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Definition amended to include "connected" (no disconnected yet), and "girth at least 7" minus "girth at least 8" formula provided by
Jason Kimberley, Dec 12 2009
A184964
Number of connected 6-regular simple graphs on n vertices with girth exactly 4.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 9, 6, 267, 3727, 483012, 69823723, 14836130862
Offset: 0
a(0)=0 because even though the null graph (on zero vertices) is vacuously 6-regular and connected, since it is acyclic, it has infinite girth.
The a(12)=1 graph is the complete bipartite graph K_{6,6}.
Connected 6-regular simple graphs with girth at least g:
A006822 (g=3),
A058276 (g=4).
Connected 6-regular simple graphs with girth exactly g:
A184963 (g=3), this sequence (g=4).
A185134
Number of, not necessarily connected, 3-regular simple graphs on 2n vertices with girth exactly 4.
Original entry on oeis.org
0, 0, 0, 1, 2, 5, 21, 103, 752, 7385, 91939, 1345933, 22170664, 401399440, 7887389438, 166897766824, 3781593764772
Offset: 0
Not necessarily connected k-regular simple graphs girth exactly 4:
A198314 (any k),
A185644 (triangle); fixed k:
A026797 (k=2), this sequence (k=3),
A185144 (k=4).
Not necessarily connected 3-regular simple graphs on 2n vertices with girth exactly g:
A185130 (triangle); fixed g:
A185133 (g=3), this sequence (g=4),
A185135 (g=5),
A185136 (g=6).
A184954
Number of connected 5-regular simple graphs on 2n vertices with girth exactly 4.
Original entry on oeis.org
0, 0, 0, 0, 0, 1, 1, 7, 388, 406824, 1125022325, 3813549359274
Offset: 0
Connected 5-regular simple graphs with girth at least g:
A006821 (g=3),
A058275 (g=4).
Connected 5-regular simple graphs with girth exactly g:
A184953 (g=3), this sequence (g=4),
A184955 (g=5).
A184974
Number of connected 7-regular simple graphs on 2n vertices with girth exactly 4.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 1, 1, 8, 741, 2887493
Offset: 0
a(0)=0 because even though the null graph (on zero vertices) is vacuously 7-regular and connected, since it is acyclic, it has infinite girth.
The a(7)=1 graph is the complete bipartite graph K_{7,7}.
Connected 7-regular simple graphs with girth at least g:
A014377 (g=3),
A181153 (g=4).
Connected 7-regular simple graphs with girth exactly g:
A184973 (g=3), this sequence (g=4).
A210709
Number of trivalent connected simple graphs with 2n nodes and girth at least 9.
Original entry on oeis.org
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18
Offset: 0
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