Vertex-transitive median graphs of non-exponential growth

摘要

We characterize vertex-transitive median graphs of non-exponential growth as the Cartesian products of finite hypercubes with finite dimensional lattice graphs. Additionally, we prove that every median graph without convex subgraphs isomorphic to K-1,K-3 or the 4-pan graph is isomorphic to the weak Cartesian product of finite paths, rays and two way infinite paths. (C) 2014 Elsevier B.V. All rights reserved.