A339160
Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) loopless multigraphs with n edges and k nodes (n >= 1, 2 <= k <= n + 1).
Original entry on oeis.org
1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 0, 1, 3, 6, 3, 1, 0, 1, 4, 11, 11, 4, 1, 0, 1, 5, 22, 33, 23, 5, 1, 0, 1, 7, 38, 89, 96, 40, 7, 1, 0, 1, 8, 63, 212, 345, 234, 70, 8, 1, 0, 1, 10, 98, 463, 1083, 1146, 546, 110, 10, 1, 0, 1, 12, 151, 943, 3068, 4739, 3505, 1169, 176, 12, 1, 0
Offset: 1
Triangle T(n,k) begins (n edges >= 1, k vertices >= 2):
1;
1, 0;
1, 1, 0;
1, 1, 1, 0;
1, 2, 2, 1, 0;
1, 3, 6, 3, 1, 0;
1, 4, 11, 11, 4, 1, 0;
1, 5, 22, 33, 23, 5, 1, 0;
1, 7, 38, 89, 96, 40, 7, 1, 0;
1, 8, 63, 212, 345, 234, 70, 8, 1, 0;
1, 10, 98, 463, 1083, 1146, 546, 110, 10, 1, 0;
1, 12, 151, 943, 3068, 4739, 3505, 1169, 176, 12, 1, 0;
...
A360866
Triangle read by rows: T(n,k) is the number of unlabeled connected loopless multigraphs with n edges on k nodes and degree >= 3 at each node, n >= 2, 1 <= k <= floor(2*n/3).
Original entry on oeis.org
0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 3, 2, 0, 1, 4, 7, 0, 1, 6, 19, 6, 0, 1, 8, 40, 37, 6, 0, 1, 10, 71, 135, 56, 0, 1, 12, 117, 366, 338, 35, 0, 1, 15, 184, 858, 1417, 494, 20, 0, 1, 17, 270, 1778, 4670, 3494, 492, 0, 1, 20, 387, 3413, 13125, 17355, 6047, 251
Offset: 2
Triangle begins:
0;
0, 1;
0, 1;
0, 1, 1;
0, 1, 3, 2;
0, 1, 4, 7;
0, 1, 6, 19, 6;
0, 1, 8, 40, 37, 6;
0, 1, 10, 71, 135, 56;
0, 1, 12, 117, 366, 338, 35;
0, 1, 15, 184, 858, 1417, 494, 20;
0, 1, 17, 270, 1778, 4670, 3494, 492;
0, 1, 20, 387, 3413, 13125, 17355, 6047, 251;
...
A002935
Number of series-reduced star graphs with n edges.
Original entry on oeis.org
1, 1, 2, 5, 9, 22, 62, 177, 560, 1939, 7067, 27331, 110871, 468684, 2057161, 9341736
Offset: 3
- N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A360870
Triangle read by rows: T(n,k) is the number of unlabeled connected multigraphs with n edges on k nodes, no cut-points and degree >= 3 at each node, loops allowed, n >= 2, 1 <= k <= floor(2*n/3).
Original entry on oeis.org
1, 1, 2, 1, 4, 1, 7, 2, 1, 10, 8, 2, 1, 14, 19, 11, 1, 18, 40, 48, 7, 1, 23, 77, 154, 70, 5, 1, 28, 132, 421, 392, 71, 1, 34, 217, 1008, 1638, 690, 35, 1, 40, 340, 2210, 5623, 4548, 767, 16, 1, 47, 510, 4477, 16745, 22657, 8594, 566, 1, 54, 742, 8557, 44698, 92844, 64716, 11247, 226
Offset: 2
Triangle begins:
1;
1, 2;
1, 4;
1, 7, 2;
1, 10, 8, 2;
1, 14, 19, 11;
1, 18, 40, 48, 7;
1, 23, 77, 154, 70, 5;
1, 28, 132, 421, 392, 71;
1, 34, 217, 1008, 1638, 690, 35;
1, 40, 340, 2210, 5623, 4548, 767, 16;
1, 47, 510, 4477, 16745, 22657, 8594, 566;
1, 54, 742, 8557, 44698, 92844, 64716, 11247, 226;
...
Row sums except first column are
A360871.
A360879
Number of unlabeled nonseparable (or 2-connected) loopless multigraphs with circuit rank n and degree >= 3 at each node.
Original entry on oeis.org
0, 1, 4, 17, 118, 1198, 17133, 311757, 6803203
Offset: 1
- Martin Dowd, Some results on reconstructibility of colored graphs, IJPAM, 95 (2014), 309-321. Gives the sequence up to a(8) in Figure 1.
- Martin Dowd, The source code of an implementation of the algorithm from the paper and data files containing the output graphs, 2024.
- Zhizheng Ye, Xuewen Huang, Chuanyu Wu, Xianglei Xue and Liang Sun, Synthesis of contracted graph for planar nonfractionated simple-jointed kinematic chain based on similarity information, Mechanism and Machine Theory, 181 (2023), 105227. Gives the sequence in Table 3 with an erroneous term a(8) = 311737.
a(8) from the paper by Martin Dowd (2014) and a(9) from Martin Dowd (personal communication) added by
Andrey Zabolotskiy, Feb 21 2024
Showing 1-5 of 5 results.
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