A058929
Number of 2-connected claw-free labeled cubic graphs with 2n nodes.
Original entry on oeis.org
0, 1, 60, 2520, 453600, 59875200, 10897286400, 6701831136000, 2623194782208000, 1338096104497152000, 1633313557551836160000, 1324107982344764897280000, 1408369399403068118016000000
Offset: 1
- G.-B. Chae, E. M. Palmer and R. W. Robinson, Computing the number of Claw-free Cubic Graphs with given Connectivity, preprint, 2001.
A084659
Number of labeled claw-free cubic graphs on 2n nodes (not necessarily connected).
Original entry on oeis.org
1, 0, 1, 60, 2555, 466200, 62791575, 14536021500, 8381453705625, 3284480337138000, 1942832950684250625, 2143745512307546647500, 1743194710893176557891875, 2022583790860881671548125000
Offset: 0
- R. J. Mathar, Table of n, a(n) for n = 0..26 Nov 26 2018
- B. D. McKay, Edgar M. Palmer, Ronald C. Read and Robert W. Robinson. The asymptotic number of claw-free cubic graphs, Discrete Math., 272 (2003), 107-118.
- Edgar M. Palmer, Ronald C. Read and Robert W. Robinson. Counting claw-free cubic graphs, SIAM J. Discrete Math. 16 (2002), 65-73.
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cfc[0] := 1; cfc[1] := 0; cfc[n+1] := (6*n-5)*binomial(2*n+1,3)*cfc[n-1] + 60*(2*n^2-7)*binomial(2*n+1,5)*cfc[n-2] + 420*(12*n-31)*binomial(2*n+1,7)*cfc[n-3] - 60480*(4*n-19)*binomial(2*n+1,9)*cfc[n-4] - 3326400*(6*n^2-54*n+127)*binomial(2*n+1,11)*cfc[n-5] - 172972800*(9*n^2-108*n+347)*binomial(2*n+1,13)*cfc[n-6] - 54486432000*(n-1)*binomial(2*n+1,15)*cfc[n-7] + 59281238016000*(n-7)*binomial(2*n+1,17)*cfc[n-8] + 422378820864000*(18*n-97)*binomial(2*n+1,19)*cfc[n-9] + 6563766876226560000*binomial(2*n+1,21)*cfc[n-10] + 673229602575129600000*binomial(2*n+1,23)*cfc[n-11];
A084656
Number of unlabeled connected claw-free cubic graphs on 2n vertices.
Original entry on oeis.org
0, 1, 1, 1, 1, 3, 3, 5, 11, 15, 27, 54, 94, 181, 369, 731, 1502, 3187
Offset: 1
K_4 is claw-free and so a(2) = 1, while the triangular prism is the only claw-free cubic graph on 6 vertices, so a(3) = 1.
- A. Itzhakov and M. Codish, Breaking Symmetries with High Dimensional Graph Invariants and their Combination, Proceedings of the 20th International Conference on the Integration of Constraint Programming, Artificial Intelligence, and Operations Research (2023).
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