A leaf of a tree is a vertex of degree one in an unrooted tree. In a rooted tree, the usual convention instead calls a vertex a leaf of a tree when it has no children, so the one-vertex rooted tree has a leaf even though its degree is zero. Every finite tree with at least two vertices has at least two leaves: the endpoints of a longest simple path cannot have an unused neighbour without extending that path. Removing a leaf and its incident edge leaves a tree, a useful step in mathematical induction.
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