Question

If we have a tree of n nodes how many edges will it have

Answer 1

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Answer 2

A tree of n nodes will have n edges.

Suppose the tree with n nodes has n - 1 edges

Let T be the tree with n + 1 nodes

T must have a leaf i.e. a node v such that degv = 1

Remove v and the 1 edge incident at v

The remainder is a tree which has n vertices

So it has n - 1 edges

Therefore, T must have had (n - 1) + 1 = n edges.