Definition
We call a connected undirected graph without cycles a tree.![](images/graf.png)
Properties of trees
Theorem 1
Let G=(V,U) be an undirected graph. The following statements are equivalent:- G is a tree
- Any two vertices in G are joined by a unique simple chain
- G is minimally connected (if we suppress an edge, the resulting graph is disconnected)
- G is connected and has |V|-1 edges
- G is acyclic and has |V|-1 edges
- G is maximally acyclic (if we add an edge, the resulting graph contains cycles)