linguistic:voice_change
Tree

A tree is an undirected graph G that satisfies any of the following equivalent conditions:

If G has finitely many vertices, say n of them, then the above statements are also equivalent to any of the following conditions:

As elsewhere in graph theory, the order-zero graph (graph with no vertices) is generally not considered to be a tree: while it is vacuously connected as a graph (any two vertices can be connected by a path), it is not 0-connected (or even (−1)-connected) in algebraic topology, unlike non-empty trees, and violates the "one more vertex than edges" relation. It may, however, be considered as a forest consisting of zero trees.

An internal vertex (or inner vertex) is a vertex of degree at least 2. Similarly, an external vertex (or outer vertex, terminal vertex or leaf) is a vertex of degree 1. A branch vertex in a tree is a vertex of degree at least 3.

An irreducible tree (or series-reduced tree) is a tree in which there is no vertex of degree 2 (enumerated at sequence A000014 in the OEIS).