Use mathematical induction to prove that an undirected tree T of order n has n-1 edges

Use mathematical induction to prove that an undirected tree T of order n has n-1 edges

Proof:
When n=1, because the tree T has no loops, the number of edges of T is m=0 and m=n-1 holds.
It is true when n=k. When n=k+1, then T has at least two leaves. Let v be a leaf, delete v and its adjacent edges. At this time, the tree has n-1 vertices and m-1 edges. There is an induction hypothesis that $(m-1)=(n-1)-1.$ I.e.,$m=n-1$ .
Proved.