Recursive tree

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In graph theory, a recursive tree (i.e., unordered tree) is a labeled, rooted tree. A size-n recursive tree's vertices are labeled by distinct positive integers 1, 2, …, n, where the labels are strictly increasing starting at the root labeled 1. Recursive trees are non-planar, which means that the children of a particular vertex are not ordered; for example, the following two size-3 recursive trees are equivalent: ₃/¹\₂ = ₂/¹\₃.

Recursive trees also appear in literature under the name Increasing Cayley trees.