Menu
Home
People
Places
Arts
History
Plants & Animals
Science
Life & Culture
Technology
Reference.org
Recursive tree
open-in-new
<p>In <a href="/facts/Graph_theory/VVPCd4TX">graph theory</a>, a recursive tree (i.e., unordered tree) is a <a href="/facts/Graph_labeling/ux5jKRD7">labeled</a>, rooted <a href="/facts/Tree_(graph_theory)/TCWk4Joy">tree</a>. A size-n recursive tree's <a href="/facts/Vertex_(graph_theory)/WhlWmL3o">vertices</a> are labeled by distinct <a href="/facts/Positive_integer/u65og8JE">positive integers</a> 1, 2, …, <i>n</i>, where the labels are strictly increasing starting at the root labeled 1. Recursive trees are <a href="/facts/Planar_graph/plREagr9">non-planar</a>, 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. </p><p>Recursive trees also appear in literature under the name <i>Increasing Cayley trees</i>. </p>