Unit distance graphs and algebraic integers
Danylo Radchenko

TL;DR
This paper investigates the structure of unit distance graphs formed by finitely generated additive subgroups of the plane, providing answers to a specific question about vertex degrees posed by Brass.
Contribution
It offers new insights into the properties of unit distance graphs related to algebraic integers and finitely generated groups, addressing an open question in the field.
Findings
Resolved Brass's question on vertex degrees
Characterized unit distance graphs of finitely generated subgroups
Connected algebraic integers to geometric graph properties
Abstract
We answer a question of Brass about vertex degrees in unit distance graphs of finitely generated additive subgroups of .
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