A184940
Irregular triangle C(n,g) counting the connected 4-regular simple graphs on n vertices with girth exactly g.
Original entry on oeis.org
1, 1, 2, 5, 1, 16, 0, 57, 2, 263, 2, 1532, 12, 10747, 31, 87948, 220, 803885, 1606, 8020590, 16828, 86027734, 193900, 983417704, 2452818, 11913817317, 32670329, 1, 152352034707, 456028472, 2, 2050055948375, 6636066091, 8, 28466137588780, 100135577616, 131
Offset: 5
1;
1;
2;
5, 1;
16, 0;
57, 2;
263, 2;
1532, 12;
10747, 31;
87948, 220;
803885, 1606;
8020590, 16828;
86027734, 193900;
983417704, 2452818;
11913817317, 32670329, 1;
152352034707, 456028472, 2;
2050055948375, 6636066091, 8;
28466137588780, 100135577616, 131;
Connected 4-regular simple graphs with girth exactly g: this sequence (triangle); chosen g:
A184943 (g=3),
A184944 (g=4),
A184945 (g=5),
A184946 (g=6).
Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth exactly g:
A198303 (k=3), this sequence (k=4),
A184950 (k=5),
A184960 (k=6),
A184970 (k=7),
A184980 (k=8).
A184941
Irregular triangle C(n,g) counting the connected 4-regular simple graphs on n vertices with girth at least g.
Original entry on oeis.org
1, 1, 2, 6, 1, 16, 0, 59, 2, 265, 2, 1544, 12, 10778, 31, 88168, 220, 805491, 1606, 8037418, 16828, 86221634, 193900, 985870522, 2452818, 11946487647, 32670330, 1, 152808063181, 456028474, 2, 2056692014474, 6636066099, 8, 28566273166527, 100135577747, 131
Offset: 5
1;
1;
2;
6, 1;
16, 0;
59, 2;
265, 2;
1544, 12;
10778, 31;
88168, 220;
805491, 1606;
8037418, 16828;
86221634, 193900;
985870522, 2452818;
11946487647, 32670330, 1;
152808063181, 456028474, 2;
2056692014474, 6636066099, 8;
28566273166527, 100135577747, 131;
Connected 4-regular simple graphs with girth at least g: this sequence (triangle); chosen g:
A006820 (g=3),
A033886 (g=4),
A058343 (g=5),
A058348 (g=6).
Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth at least g:
A185131 (k=3), this sequence (k=4),
A184951 (k=5),
A184961 (k=6),
A184971 (k=7),
A184981 (k=8).
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).
A185044
Number of disconnected 4-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, 0, 0, 0, 0, 1, 0, 2, 2, 15, 35, 247, 1692, 17409, 197924, 2492824, 33117880, 461597957, 6709514218, 101153412903, 1597440868898
Offset: 0
Disconnected 4-regular simple graphs with girth exactly g:
A185043 (g=3), this sequence (g=4).
Disconnected k-regular simple graphs with girth exactly 4:
A185034 (k=3), this sequence (k=4).
a(31) corrected by the author, propagated from
A185244, Jan 05 2013
A184946
Number of connected 4-regular simple graphs on n vertices with girth exactly 6.
Original entry on oeis.org
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, 1, 0, 1, 0, 4, 0, 19, 0, 1272, 25, 494031, 13504
Offset: 0
Connected 4-regular simple graphs with girth exactly g:
A184943 (g=3),
A184944 (g=4),
A184945 (g=5), this sequence (g=6).
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