Markov Number Graphs Extended to all Integer Triples

TL;DR

This paper explores the extension of Markov number graphs to all integer triples, revealing a finite classification of equivalence classes with distinct properties.

Contribution

It introduces a new framework for analyzing Markov number graphs beyond triples satisfying the Markov equation, identifying finite classes with unique characteristics.

Findings

Finite number of equivalence classes of graphs

Distinct properties identified for each class

Extension of Markov graphs to all integer triples

Abstract

We study the graphs generated when the formula for linking Markov triples is applied to general triples of integers. We find there are a finite number of equivalence classes of graphs, each with particular properties.