A graph with n vertices is a tree if and

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.)

PROBLEM SET 23.3: