Nodes and Edges
A tree $T$ is a pair $(V, E)$, where $V$ is a set of nodes (vertices) and $E$ is a set of edges.
The Root
There is a unique node $r \in V$ called the root, which has no parent.
Parent-Child Relation
Every node $v \in V \setminus \{r\}$ has exactly one parent node $u$.
Properties
The graph is connected and acyclic. A tree with $n$ nodes has $n-1$ edges.
Live Rule Check
One root node
One parent per non-root node
The graph must be connected
Cannot contain cycles