Tree

Remarks

Let $T$ be a finite graph with $n \ge 1$ vertices. Then these conditions are equivalent: $T$ is a tree; $T$ is connected with $n - 1$ edges; $T$ is acyclic with $n - 1$ edges. A graph is a tree if and only if any two vertices are joined by exactly one path. The node unique paths in trees states this. The path graphs and the stars $K_{1,n}$ are trees.