Extend the argument given in the proof of Lemma 10.4.1 to show that a tree with more than one vertex has at least two vertices of degree 1.
To prove:
A tree with more than one vertex has at least two vertices of degree 1.
Given:
The lemma, any tree that has more than one vertex has at least one vertex of degree 1.
Proof:
Let T be a tree with more than 1 vertex.
Let
While
Let then
Repeat until you obtain that