A290667 Number of asymmetric equicolorable (unrooted) trees with 2*n vertices.

0, 0, 0, 1, 4, 19, 84, 378, 1727, 8126, 39055, 191902, 960681

Offset: 1

Author

John P. McSorley, Aug 08 2017

Keywords

• nonn
• more

Comments

Any tree with 2n vertices is a bipartite graph with s vertices in one part and t vertices in the other part, where s <= t and s + t = 2n. We count trees with s = t = n, and which are asymmetric, that is, their only automorphism is the identity automorphism. These are also called identity trees.

Examples

			a(3) = 0 because there are six trees with 6 vertices, but only three of these have s = t = n = 3, and none of these three is asymmetric. The fourth term a(4) = 1 because there are nine trees with 8 vertices with s = t = n = 4 but only 1 is asymmetric, namely tree T46. See "Atlas of Graphs", page 65.
		

References

• R. C. Read and R. J. Wilson, Atlas of Graphs, Oxford Science Publications, Clarendon Press, OUP, 2004.

Links

• F. Hüffner, tinygraph, software for generating integer sequences based on graph properties.
• Austin Mohr, Unlabeled Trees.

Crossrefs

Cf. A119856 (equicolorable trees with 2n vertices), A000220 (asymmetric trees with n vertices).

Extensions

a(10)-a(13) added using tinygraph by Falk Hüffner, Jul 25 2019