2001/12/20 by Claudio Destri, Luca Donetti
Computer Science · Mathematics · Physics and Astronomy · #Interconnection Networks and Systems #Stochastic processes and statistical mechanics #Topological and Geometric Data Analysis #cond-mat
paper · pdf · doi:10.1088/0305-4470/35/25/301
published as J. Phys. A 35 (2002) 5147-5163 · 15 pages, revtex4, 4 eps figures, submitted to Journal of Physics A
arxiv created 2001/12/20 · openalex publication_date 2002/06/14 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Bounded infinite graphs are defined on the basis of natural physical requirements. When specialized to trees, this definition leads to a natural conjecture that the average connectivity dimension of bounded trees cannot exceed two. We verify that this bound is saturated by a class of random trees, in which case we also derive explicit expressions for the growth probabilities.