What are the 9 non-isomorphic rooted trees with 5 vertices?

Question

I'm wondering what the non-isomorphic rooted trees with 5 vertices look like. According to the textbook I'm reading, there are 9 of them but I don't know what they look like or how to draw them or if I'm just misunderstanding the question.

Thanks for you help!

Answer 1

These are the 9 non-isomorphic rooted trees with 5 vertices.

Answer 2

3 classes of drawings:

• a path on 5 vertices produces 3 rooted trees
• a path on 4 vertices and one additional edge to make 1 vertex of degree 3 yields 4 more
• a vertex of degree 4 surrounded by leaves yields 2 more