Tree statistics from Matula numbers

TL;DR

This paper explores how properties of rooted trees can be derived directly from their unique Matula numbers, establishing a mathematical link between number theory and tree structures.

Contribution

It introduces methods to extract various tree properties directly from Matula numbers, providing a novel approach to analyze rooted trees through number theory.

Findings

Tree properties can be derived from Matula numbers

Matula numbers establish a one-to-one correspondence with rooted trees

New techniques for analyzing tree structures using number theory

Abstract

There is a one-to-one correspondence between natural numbers and rooted trees; the number is called the Matula number of the rooted tree. We show how a large number of properties of trees can be obtained directly from the corresponding Matula number.