A022562
Number of connected claw-free unlabeled graphs on n nodes.
Original entry on oeis.org
1, 1, 2, 5, 14, 50, 191, 881, 4494, 26389, 184749, 1728404, 23805256, 491544474, 14491876320
Offset: 1
- R. Faudree, E. Flandrin and Z. Ryjacek, Claw-free graphs - a survey, Discr. Math., 164 (1997), 87-147.
- F. Hüffner, tinygraph, software for generating integer sequences based on graph properties, version 8489dde.
- Gordon Royle, 1728404 distinct 12-vertex connected clawfree graphs
- Gordon Royle, g6 format
- Eric Weisstein's World of Mathematics, Claw-Free Graph
- Wikipedia, Claw-free Graph
-
EulerInvTransform[seq_] := Module[{final = {}}, For[i = 1, i <= Length[seq], i++, AppendTo[final, i*seq[[i]] - Sum[final[[d]]*seq[[i - d]], {d, i - 1}]]]; Table[Sum[MoebiusMu[i/d]*final[[d]], {d, Divisors[i]}]/i, {i, Length[seq]}]];
A086991 = Cases[Import["https://oeis.org/A086991/b086991.txt", "Table"], {, }][[All, 2]];
EulerInvTransform[A086991] (* Jean-François Alcover, Aug 20 2019, code due to Gus Wiseman *)
Term a(15) added using tinygraph by
Falk Hüffner, Jan 12 2016
A057848
Number of 1-connected claw-free cubic graphs with 2n nodes.
Original entry on oeis.org
0, 1, 60, 2520, 453600, 59875200, 13621608000, 8009505504000, 3123380227968000, 1832279324908032000, 2054813830468439040000, 1665031453088810526720000, 1925086583971531588608000000
Offset: 1
- Sean A. Irvine, Table of n, a(n) for n = 1..100 (terms 1..30 from G.-B. Chae, term 30 corrected by Sean A. Irvine)
- G.-B. Chae, Home page
- G.-B. Chae, Counting labeled claw-free cubic graphs by connectivity, Discrete Mathematics 308 (2008) 5136-5143.
- G.-B. Chae, E. M. Palmer and R. W. Robinson, Computing the number of Claw-free Cubic Graphs with given Connectivity, Preprint, 2000. (Annotated scanned copy)
A058931
Number of 3-connected claw-free cubic graphs with 2n nodes.
Original entry on oeis.org
0, 1, 60, 0, 0, 19958400, 0, 0, 622452999168000, 0, 0, 258520167388849766400000, 0, 0, 675289572271869736778268672000000, 0, 0, 7393367369949286697176489031997849600000000, 0, 0
Offset: 1
- G.-B. Chae (chaegabb(AT)pilot.msu.edu), E. M. Palmer and R. W. Robinson, Computing the number of Claw-free Cubic Graphs with given Connectivity, preprint, 2001.
A058930
Number of 3-connected claw-free cubic graphs with 6n nodes.
Original entry on oeis.org
0, 60, 19958400, 622452999168000, 258520167388849766400000, 675289572271869736778268672000000, 7393367369949286697176489031997849600000000
Offset: 0
- G.-B. Chae (chaegabb(AT)pilot.msu.edu), E. M. Palmer and R. W. Robinson, Computing the number of Claw-free Cubic Graphs with given Connectivity, preprint, 2001.
A084657
Number of unlabeled 2-connected claw-free cubic graphs on 2n vertices.
Original entry on oeis.org
0, 1, 1, 1, 1, 3, 2, 4, 8, 10, 16, 34, 51, 99, 198
Offset: 1
A058932
Number of unlabeled claw-free cubic graphs with 2n nodes and connectivity 1.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 1, 1, 3, 5, 11, 20
Offset: 1
- G.-B. Chae (chaegabb(AT)pilot.msu.edu), E. M. Palmer and R. W. Robinson, Computing the number of Claw-free Cubic Graphs with given Connectivity, preprint, 2001.
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