Tree (graph theory)

A tree is an undirected graph which is both connected and acyclic. Equivalently, a tree is a graph $G=(V,E)$ such that for any two vertices $u, v \in V$ with $u \neq v$ , there is exactly one path connecting $u$ and $v$ in $G$ . Every tree that has $|V|=n$ vertices has exactly $n-1$ edges.

The converse is also true: an undirected and connected graph with $n$ vertices and $n-1$ edges is a tree.

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Tree (graph theory)