On Matula numbers
type: Item
instance of: scholarly article
title: On Matula numbers
zbMATH Open document ID: 0854.05035
DOI: 10.1016/0012-365X(95)00182-V
author: Ivan Gutman
author: Aleksandar Ivić
published in: Discrete Mathematics
publication date: 1997-01-13T00:00:00Z
review text: There are many methods to get a one-to-one correspondence between the set of natural numbers and the set of rooted trees. One of the methods uses the Matula numbers. Let \(T\) be a rooted tree, and let \(v\) be the root of \(T\). Then the Matula number \(n(T, v)\) is determined in the following recursive manner: (1) \(n(T, v)= 1\) for the single-vertex tree. (2) Let the root \(v\) of \(T\) be of degree \(d\). Then \(T\) can be considered as being obtained by joining the roots \(v_1,\dots, v_d\) of some rooted trees \(T_1,\dots, T_d\) and \[ n(T, v)= \prod^d_{i= 1} p_{n(T_i, v_i)}, \text{ where \(p_m\) denotes the \(m\)th prime number}. \] The paper lists known characterizations of Matula numbers and corresponding rooted trees, and determines the rooted trees with maximal Matula numbers.
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C30
zbMATH DE Number: 895994
zbMATH Keywords: rooted tree
zbMATH Keywords: Matula number
reviewed by: Dietmar Cieslik
MaRDI profile type: Publication
cites work: Q4548565
cites work: On the distribution function of additive functions
cites work: Q4313516
cites work: Q4296347
full work available at URL: 0012-365x(95)00182-v
OpenAlex ID: W2020583546
description: scientific article; zbMATH DE number 895994