A graph is of parabolic or hyperbolic type if the simple random walk on the vertices is, respectively, recurrent or transient. A plane triangulation graph is C-parabolic or CP-hyperbolic if the maximal circle packing determined by the graph packs, respectively, the complex plane C or the Poincare disk D. We examine the impli- cations that (Gromov) negative curvature carries for determining type, specifically in these setting. Our main result is encased in the following theorem.
展开▼
