Horofunctions of infinite Sierpinski polygon graphs

2025/07/31 by Daniele D’Angeli, Francesco Matucci, D'Angeli, Daniele +5
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.2507.23681

openalex publication_date 2025/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Generalizing works of D'Angeli and Donno, we describe, starting from an infinite sequence over r letters with r ≠ 4i and i ∈ 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.

Citations

• The independence polynomial on recursive sequences of graphs
• Horofunctions on the Heisenberg and Cartan groups
• Rationality of the Gromov Boundary of Hyperbolic Groups
• Rational embeddings of hyperbolic groups
• Isomorphism classification of infinite Sierpinski carpet graphs
• Gromov boundaries as Markov compacta
• Busemann Points of Infinite Graphs
• Busemann points of infinite graphs

Related

• Horofunctions on Sierpiński type triangles
• Busemann points of Artin groups of dihedral type
• Groups with finitely many Busemann points
• Isomorphism classification of infinite Sierpinski carpet graphs
• An infinite clique of high-filling rays in the plane minus a Cantor set