Trees have a vertex of degree $1$ Prove that any tree has a vertex of degree $1$.
Let graph $G=(V,E)$ have $n$ vertices and $m$ edges where $m<n$. We need to prove that the minimum degree of, $\delta (G)=1$ 
Since G is connected then there exists a path from $u$ to $v$ such that $u,v \in V$. 
Is what I have said so far correct? I really don't know how to carry it on. I need a formal answer.

This is trivial: every tree has n-1 edges, where n is the number of vertices. If every vertices has degree at least 2 the sum of the degree is at least 2n.So there are at least n edges. Impossible.
