prove that a tree with n vertices
has n-1 edges
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Proof:
Consider a tree T with n vertices. Let us reconstruct the tree from the root vertex.
When the first root vertex has been added, the number of edges is zero. After the root vertex, every vertex that is added to the construction of T contributes one edge to T.
Adding the remaining n−1 vertices to the construction of T, after the root vertex, will add n−1 edges.
Therefore, after the reconstruction of T is complete, T will have n vertices and n−1 edges.
Hence Proved.
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