Prove that a tree with n vertices has n-1 edges

In this video, I will show you how to prove that a tree with n vertices or nodes has n-1 edges using proof by induction. For example, if you are given a tree with 10 vertices or nodes, then you know for sure that there are 9 edges. So, what exactly is a tree? A tree is an undirected graph that is a connected graph and has no cycles, parallel edges, or loops. I will prove this statement using mathematical statement. The induction proof that a tree of n nodes has n-1 edges is a basic theorem in graph theory which is important in both discrete math and computer science classes. If you are given a graph of n vertices with no cycles, loops, or parallel edges, and you find out that the graph has exactly n-1 edges, then you know that it is a tree.

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