# A graph with n vertices is a tree if and only if it has n - 1 edges and has no cycles. Data from Prob. 16 If a graph has no cycles, it must have at least 2 vertices of degree 1 Data from Prob. 18 A tree with n vertices has n - 1 edges. (Proof by induction.)

Chapter 23, PROBLEM SET 23.4 #20

A graph with n vertices is a tree if and only if it has n - 1 edges and has no cycles.

**Data from Prob. 16**

If a graph has no cycles, it must have at least 2 vertices of degree 1

**Data from Prob. 18**

A tree with n vertices has n - 1 edges. (Proof by induction.)

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