How do you like them apples?
How many homeomorphically irreducible trees are there on 10 vertices?
Clarification: A homeomorphically irreducible tree is one in which there is no vertex of degree two.
Image credit: blogwillhunting.com
The answer is 10.
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1 solution
[This is not a full solution.]
These are the ten possible trees:
How does one enumerate these objects algorithmically? Or to start with, how does one count the number of non-isomorphic trees?