The definition of tree is an undirected graph, which is connected and acyclic.

In graph T, when n=2, the connectivity is acyclic and the number of edges e= 1, so e=n- 1 holds.

Let n=k- 1 and the proposition holds. When n=k, because there is no loop and connectivity, the degree of the endpoint U of at least one edge is 1. Let the edge be (u, w) and delete the node u, then a connected acyclic graph T' with k- 1 nodes is obtained. By induction, it is assumed that t' e' = n'-1= the number of edges of k-2, and then the point u and the edge (u, w) are added to the graph t' to get the graph.

To sum up, the conclusion is established.