Leaf-induced subtrees of leaf-Fibonacci trees

Abstract

In analogy to a concept of Fibonacci trees, we define the leaf-Fibonacci tree of size $n$ and investigate its number of nonisomorphic leaf-induced subtrees. Denote by $f_0$ the one vertex tree and $f_1$ the tree that consists of a root with two leaves attached to it; the leaf-Fibonacci tree $f_n$ of size $n\ge 2$ is the binary tree whose branches are $f_{n-1}$ and $f_{n-2}$. We derive a nonlinear difference equation for the number $\text{N}(f_n)$ of nonisomorphic leaf-induced subtrees (subtrees induced by leaves) of $f_n$, and also prove that $\text{N}(f_n)$ is asymptotic to $1.00001887227319\dots (1.48369689570172\dots {)}^{{\varphi }^n}$ ($\varphi =$~golden ratio) as $n$ grows to infinity.

arXiv comment9 pages, 4 figures

References in corpus (1)

• Inducibility of d-ary trees