A185043
Number of disconnected 4-regular simple graphs on n vertices with girth exactly 3.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 8, 25, 88, 377, 2026, 13349, 104593, 930571, 9124627, 96699740, 1095467916, 13175254799, 167460501260, 2241576473025, 31510509517563, 464047467911837, 7143984462730072, 114749034352969037, 1919656978492976231
Offset: 0
4-regular simple graphs with girth exactly 3:
A184943 (connected), this sequence (disconnected),
A185143 (not necessarily connected).
Disconnected 4-regular simple graphs with girth exactly g: this sequence (g=3),
A185044 (g=4).
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).
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).
A186743
Number of connected regular simple graphs on n vertices with girth exactly 3.
Original entry on oeis.org
0, 0, 0, 1, 1, 1, 3, 3, 13, 21, 157, 536, 18942, 389404, 50314456, 2942196832, 1698517018391
Offset: 0
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