What are the properties of a tree?

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1. There is one and only one path between every pair of vertices in a tree, T.
2. A tree with n vertices has n-1 edges.
3. Any connected graph with n vertices and n-1 edges is a tree.
4. A graph is a tree if and only if it is minimally connected.

Therefore a graph with n vertices is called a tree if
1. G is connected and is circuit less, or
2. G is connected and has n-1 edges, or
3. G is circuit less and has n-1 edges, or
4. There is exactly one path between every pair of vertices in G, or
5. G is a minimally connected graph.
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