A292405
Number of 3-regular maps with 2n vertices on the torus, up to orientation-preserving and orientation-reversing isomorphisms.
Original entry on oeis.org
1, 5, 40, 450, 6370, 104498, 1843324, 33778574, 632053347, 11983323029, 229304019611, 4419024507187, 85653324334312, 1668284177327594, 32629561950146399
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part II: Enumeration of Unsensed Maps, arXiv preprint arXiv:1709.03230 [math.CO], 2017.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part II: Unsensed maps, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 600-614.
A292110
Number of 6-regular maps with n vertices on the torus, up to orientation-preserving and orientation-reversing isomorphisms.
Original entry on oeis.org
3, 61, 1936, 89986, 4791784, 272005507, 15929826713, 951610091294, 57659992554993, 3532378891197016, 218331197907776846, 13594369669588615612
Offset: 1
- E. Krasko, A. Omelchenko, Enumeration of r-regular Maps on the Torus. Part II: Enumeration of Unsensed Maps, arXiv preprint arXiv:1709.03230 [math.CO], 2017. See Table 1, p. 20.
- E. Krasko, A. Omelchenko, Enumeration of r-regular maps on the torus. Part II: Unsensed maps, Discrete Mathematics, Volume 342, Issue 2, February 2019, pp. 600-614.
A301425
Number of plane 5-regular simple connected graphs with 2n vertices.
Original entry on oeis.org
1, 0, 1, 1, 6, 14, 98, 529, 4035, 31009, 252386, 2073769, 17277113
Offset: 6
There is only a(6) = 1 planar 5-regular simple connected graph with 2n = 12 vertices, which is the icosahedral graph, cf. MathWorld link. If we label the vertices 1, ..., 9, A, B, C, they are connected as follows: 1 -> {2 3 4 5 6}, 2 -> {1 6 7 8 3}, 3 -> {1 2 8 9 4}, 4 -> {1 3 9 A 5}, 5 -> {1 4 A B 6}, 6 -> {1 5 B 7 2 }, 7 -> {2 6 B C 8}, 8 -> {2 7 C 9 3}, 9 -> {3 8 C A 4}, A -> {4 9 C B 5}, B -> {5 A C 7 6}, C -> {7 B A 9 8}.
For other numbers of vertices, the number of plane 5-regular simple connected graphs is as follows:
14 vertices: 0 graphs,
16 vertices: 1 graph,
18 vertices: 1 graph,
20 vertices: 6 graphs,
22 vertices: 14 graphs,
24 vertices: 98 graphs,
26 vertices: 529 graphs,
28 vertices: 4035 graphs,
30 vertices: 31009 graphs,
32 vertices: 252386 graphs,
34 vertices: 2073769 graphs,
36 vertices: 17277113 graphs. (From the McKay web page.)
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