Theorem 16. 1 Let G =

(1)G is a tree.

(2) There is a unique path between any two vertices in graph G. 。

(3) There is no cycle in G, and m=n- 1.

(4)G connected, m=n- 1.

(5)G is connected, and any edge in G is a bridge.

(6) There is no cycle in G, but a new edge is added between any two different vertices, and a unique cycle with a new edge is obtained in the obtained graph.