Horofunctions of infinite Sierpinski polygon graphs

TL;DR

This paper generalizes the study of horofunction boundaries for infinite Sierpinski polygon graphs, describing their limits and isomorphism classes using dihedral groups, and analyzing Busemann points.

Contribution

It introduces a new class of infinite graphs based on sequences over r letters and characterizes their horofunction boundaries and isomorphism classes.

Findings

Describes pointed Gromov-Hausdorff limits of the graphs

Classifies isomorphism classes using dihedral groups

Analyzes Busemann and non-Busemann points in the boundary

Abstract

Generalizing works of D'Angeli and Donno, we describe, starting from an infinite sequence over $r$ letters with $r \neq 4i$ and $i \in \mathbb{N}$, a sequence of pointed finite graphs. We study the pointed Gromov-Hausdorff limit graphs giving a description of isomorphim classes in terms of dihedral groups and providing insights on the horofunction boundaries in terms of Busemann and non-Busemann points.