The Rotor-Router Group of Directed Covers of Graphs

  • Wilfried Huss Institute of Discrete Mathematics Vienna University of Technology Wiedner Hauptstrasse 8-10 1040 Vienna
  • Ecaterina Sava Department of Mathematics C Graz University of Technology Steyrergasse 30/III 8010 Graz
Keywords: finite graphs, directed covers, periodic trees, rotor-router walks, rotor-router group, sandpile group


A rotor-router walk is a deterministic version of a random walk, in which the walker is routed to each of the neighbouring vertices in some fixed cyclic order. We consider here directed covers of graphs (called also periodic trees) and we study several quantities related to rotor-router walks on directed covers. The quantities under consideration are: order of the rotor-router group, order of the root element in the rotor-router group and the connection with random walks.
Article Number