Prove the following Theorem. If $G$ is a connected graph with $n$ vertices and $n - 1$ edges, then $G$ is a tree.
I am still new to proof methods and not sure if this is the correct use of induction.
Base case: $n = 1$. Here, $G$ has $0$ edges and is a tree.
Assume every connected graph with $k$ vertices and $k-1$ edges is a tree.
Let $G$ be a connected graph with $k+1$ vertices that contains at least one cycle (no amount of edges are specified).
Let $m$ be the number of edges removed. Remove edges from each cycle to form a new graph $G'$.
$G'$ is a tree with $k-1$ edges and $k+1$ vertices. $G$ has $k-1+m$ edges.
If $m=0$ then $G' = G$ and $G$ is a tree.