TL;DR
This paper explores properties of Matula numbers and the GIM function, linking them to coding theory to derive results about rooted trees and prime number coding.
Contribution
It demonstrates how coding theorems can be used to easily derive properties of the GIM function related to Matula numbers.
Findings
Properties of the GIM function can be obtained trivially from coding theorems.
A prefix-free code for primes with specific codelengths is constructed.
Connections between prime coding and tree enumeration are established.
Abstract
In SIAM Review 10, page 273, D. W. Matula described a bijection between N and the set of topological rooted trees; the number is called the Matula number of the rooted tree. The Gutman-Ivic-Matula (GIM) function g(n) computes the number of edges of the unique tree with Matula number n. Since there is a prefix-free code for the set of prime numbers such that the codelength of each prime p is 2g(p), we show how some properties of the GIM function can be obtained trivially from coding theorems.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Graph theory and applications · Advanced Graph Theory Research