2013/11/18 by Danny Calegari, Koji Fujiwara, Calegari, Danny +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #math.GR #math.GT
paper · pdf · doi:10.48550/arxiv.1311.4450
12 pages
arxiv created 2013/11/18 · openalex publication_date 2013/11/18 · arxiv updated 2013/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This note addresses some questions that arise in the series of works by Kyoji Saito on the growth functions of graphs. We study "hyperbolike" graphs, which include Cayley graphs of hyperbolic groups. We generalize some well-known results on hyperbolic groups to the hyperbolike setting, including rationality of generating functions, and sharp estimates on the growth rate of vertices. We then apply these results to confirm a conjecture of Saito on the "opposite series", which was originally posed for hyperbolic groups.