Let $ G $ be a tree with $ n $ vertices. Show that the following statements are equivalent:
a) $ G $ is the path with $ n $ vertices.
b) $ G $ has a maximum degree of two.
c) $ G $ has exactly two vertices of degree one.
The usual thing would be to show $ a \rightarrow b \rightarrow c \rightarrow a $. I think it would be easier to show $ a \rightarrow c \rightarrow b \rightarrow a $
If $ a \rightarrow c $ is easy, because if $ G $ is the path with $ n $ vertices, the initial and final vertex are the only ones with degree 1.
For the rest of the implications, what are your suggestions?