(data structure)

**Definition:**
A variant of a *binary tree* where a tree of order n (n>1) has a left subtree of order n-1 and a right subtree of order n-2. An order 0 Fibonacci tree has no *nodes*, and an order 1 tree has 1 node.

**Generalization** (I am a kind of ...)

*binary tree*, *AVL tree*.

**Aggregate parent** (I am a part of or used in ...)

*Fibonaccian search*.

**Aggregate child** (... is a part of or used in me.)

*Fibonacci number*.

*Note:
A Fibonacci tree of order n has F(n+2)-1 nodes, where F(n) is the n ^{th} Fibonacci number. A Fibonacci tree is the most unbalanced AVL tree allowed.*

Author: PEB

[Knuth98, 3:417, Sect. 6.2.1].

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Entry modified 4 January 2010.

HTML page formatted Fri Feb 23 10:06:07 2018.

Cite this as:

Paul E. Black, "Fibonacci tree", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 4 January 2010. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/fibonacciTree.html