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Let G = (V,E) be a graph with n vertices and e edges. Show that the...

Let G = (V,E) be a graph with n vertices and e edges. Show that the following statements are equivalent:

1. G is a tree

2. G is connected and n = e + 1

3. G has no cycles and n = e + 1

4. If u and v are vertices in G, then there exists a unique path connecting u and v.

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