A361361
Triangle read by rows: T(n,k) is the number of bicolored cubic graphs on 2n unlabeled vertices with k vertices of the first color, n >= 0, 0 <= k <= 2*n.
Original entry on oeis.org
1, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 5, 5, 5, 2, 2, 6, 11, 33, 48, 66, 48, 33, 11, 6, 21, 68, 257, 556, 950, 1071, 950, 556, 257, 68, 21, 94, 510, 2443, 7126, 15393, 23644, 27606, 23644, 15393, 7126, 2443, 510, 94, 540, 4712, 27682, 102122, 270957, 526783, 781292, 887305, 781292, 526783, 270957, 102122, 27682, 4712, 540
Offset: 0
Triangle begins:
1
0, 0, 0;
1, 1, 1, 1, 1;
2, 2, 5, 5, 5, 2, 2;
6, 11, 33, 48, 66, 48, 33, 11, 6;
21, 68, 257, 556, 950, 1071, 950, 556, 257, 68, 21;
...
A361407
Number of connected cubic graphs on 2n unlabeled vertices rooted at a vertex.
Original entry on oeis.org
0, 1, 2, 10, 64, 490, 4595, 51063, 657623, 9592204, 155630924, 2771922417, 53673859357, 1121581872170, 25143397213226, 601751140758134, 15310778492310274, 412656423154230159, 11743600063060974656, 351882591907696156959
Offset: 1
A361408
Number of connected cubic graphs on 2n unlabeled vertices rooted at a pair of indistinguishable vertices.
Original entry on oeis.org
0, 1, 5, 31, 248, 2382, 27233, 359800, 5364193, 88622485, 1602171855, 31410476113, 663240471075, 15001046054183, 361775504849332, 9266474332849318, 251217335356943672, 7186461542458525108, 216332059500870350414, 6835872042063656823802
Offset: 1
A321305
Triangle T(n,f): the number of signed cubic graphs on 2n vertices with f edges of the first sign.
Original entry on oeis.org
1, 0, 0, 0, 0, 1, 1, 2, 3, 2, 1, 1, 2, 3, 8, 16, 21, 21, 16, 8, 3, 2, 5, 14, 57, 152, 313, 474, 551, 474, 313, 152, 57, 14, 5, 19, 91, 491, 1806, 5034, 10604, 17318, 22033, 22033, 17318, 10604, 5034, 1806, 491, 91, 19, 85, 706, 4981, 23791, 84575, 229078, 487020, 825127, 1127783, 1250632, 1127783, 825127, 487020, 229078, 84575, 23791, 4981, 706, 85
Offset: 0
The triangle starts:
0 vertices: 1
2 vertices: 0,0,0,0
4 vertices: 1,1,2,3,2,1,1
6 vertices: 2,3,8,16,21,21,16,8,3,2
8 vertices: 5,14,57,152,313,474,551,474,313,152,57,14,5
10 vertices: 19,91,491,1806,5034,10604,17318,22033,22033,17318,10604,5034,1806,491,91,19
A361403
Number of bicolored connected cubic graphs on 2n unlabeled vertices.
Original entry on oeis.org
1, 0, 5, 23, 247, 4660, 124480, 4286155, 177173770, 8460721770, 456369771864, 27394102475517, 1809905002448020, 130479709461582679, 10191059146232826353, 857183200472049855001, 77244717697104310952411, 7424434373914632379955822, 758150225111024064264853603, 81967014740890327829104517614, 9353488650500180241693235592248
Offset: 0
Cf.
A361362 (not necessarily connected).
A361406
Number of bicolored connected cubic graphs on 2n unlabeled vertices with n vertices of each color.
Original entry on oeis.org
1, 0, 1, 5, 63, 1052, 27336, 882321, 34455134, 1558650424, 80016369538, 4589908631503, 290839634055722, 20171917072658395, 1519875854413728667, 123616508830454828043, 10794216583730162449785, 1007179737486515827821590, 100007950522974604304016627, 10529173417583858651114779790, 1171605981584666223513790021758
Offset: 0
a(1) = 1 since the only cubic graph on 4 vertices is the complete graph. The bicolored graphs are indistinguishable whichever 2 vertices are colored in the first color.
Showing 1-6 of 6 results.
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