A184961
Irregular triangle C(n,g) read by rows, counting the connected 6-regular simple graphs on n vertices with girth at least g.
Original entry on oeis.org
1, 1, 4, 21, 266, 7849, 1, 367860, 0, 21609300, 1, 1470293675, 1, 113314233808, 9, 9799685588936, 6
Offset: 7
Triangle begins:
1;
1;
4;
21;
266;
7849, 1;
367860, 0;
21609300, 1;
1470293675, 1;
113314233808, 9;
9799685588936, 6;
Connected 6-regular simple graphs with girth at least g: this sequence (triangle); chosen g:
A006822 (g=3),
A058276 (g=4).
Connected 6-regular simple graphs with girth exactly g:
A184960 (triangle); chosen g:
A184963 (g=3),
A184964 (g=4).
Triangular arrays C(n,g) counting connected simple k-regular graphs on n vertices with girth at least g:
A185131 (k=3),
A184941 (k=4),
A184951 (k=5), this sequence (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).
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