A digraph is said to be highly arc transitive if its automorphism group acts transitively on the set of s-arcs for all s¿ 0. The set of descendants of a directed line is de.ned as the set of all… (More)

A directed Cayley graph X is called a digraphical regular representation (DRR) of a group G if the automorphism group of X acts regularly on X . Let S be a finite generating set of the infinite… (More)

The study of infinite graphs has many aspects and various connections with other fields. There are the classical graph theoretic problems in infinite settings (see the survey by Thomassen [49]);… (More)

Criteria for quasi-isometry between trees and general graphs as well as for quasi-isometries between metrically almost transitive graphs and trees are found. Thereby we use different concepts of… (More)

Let D be a locally finite, connected, 1-arc transitive digraph. It is shown that the reachability relation is not universal inD providedthat the stabilizer of an edge satisfies certain conditions… (More)

Several results on the action of graph automorphisms on ends and fibers are generalized for the case of metric ends. This includes results on the action of the automorphisms on the end space,… (More)

We define for a compactly generated totally disconnected locally compact group a graph, called a rough Cayley graph, that is a quasi-isometry invariant of the group. This graph carries information… (More)