TY - JOUR
T1 - Highly arc transitive digraphs
T2 - Reachability, topological groups
AU - Malnič, Aleksander
AU - Marušič, Dragan
AU - Möller, Rögnvaldur G.
AU - Seifter, Norbert
AU - Trofimov, Vladimir
AU - Zgrablič, Boris
PY - 2005/1
Y1 - 2005/1
N2 - 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 with prime in- or out-degree. Two different aspects of the connection between highly arc transitive digraphs and the theory of totally disconnected locally compact groups are also considered.
AB - 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 with prime in- or out-degree. Two different aspects of the connection between highly arc transitive digraphs and the theory of totally disconnected locally compact groups are also considered.
UR - http://www.scopus.com/inward/record.url?scp=4644329523&partnerID=8YFLogxK
U2 - 10.1016/j.ejc.2004.02.006
DO - 10.1016/j.ejc.2004.02.006
M3 - Article
AN - SCOPUS:4644329523
SN - 0195-6698
VL - 26
SP - 19
EP - 28
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
IS - 1
ER -