Rögnvaldur G. Möller

Learn 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]); there are special graph theoretical questions which have no direct analogues for finite graphs, such as questions about ends (see [7], [44] and the monograph [6]);(More)
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 vertices that can be reached by a directed path from some vertex in the line. The structure of the subdigraph in a locally .nite highly arc transitive digraph(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 cyclic group Z. We show that a directed Cayley graph X (Z, S) is a DRR of Z if and only if S 6= S−1. If X (Z, S) is not a DRR we show that Aut (X (Z, S)) = D∞. As a(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 thickness for graphs, ends and end spaces. A metrically almost transitive graph is quasi-isometric to a tree if and only if it has only thin metric ends (in the(More)
Let D be a locally finite, connected, 1-arc transitive digraph. It is shown that the reachability relation is not universal in D provided that the stabilizer of an edge satisfies certain conditions which seem to be typical for highly arc transitive digraphs. As an implication, the reachability relation cannot be universal in highly arc transitive digraphs(More)