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.

How you make the argument will depend to some extent on what you already know about trees. One approach that uses nothing beyond the definition — a tree is a connected, acyclic graph — is to show that if $G$ has no vertex of degree $1$, then you can construct a cycle in $G$. Start at any vertex and keep moving to a new one as long as you can; there are only finitely many vertices altogether, so at some point ...
