## Rögnvaldur Möller (19/09/16)

Math Colloquium

### Speaker: Rögnvaldur Möller, University of Iceland

### Title: Highly-arc-transitie digraphs of prime out-valency

Location: V-158, VRII

Time: Monday 19 September at 15:00

### Abstract:

Joint work with Primoz Potocnik, Ljubljana, and Norbert Seifter, Leoben.

The concept of a highly-arc-transitive digraph was defined by Cameron, Praeger and Wormald in a paper that appeared in 1993. Examples constructed by various people have shown that suggestions put forward in that paper are wrong. But if it assumed that the highly-arc-transitive digraph has prime out-valency then some of the suggestions of Cameron, Praeger and Wormald are correct. The second part of the talk is about a general method to construct k-arc-transitive digraphs that are not (k+1)-arc-transitive. This construction gives examples that limit the possibilities of extending the results in the first part and also give examples of digraphs with polynomial growth that are k-arc-transitive but not (k+1)-arc-transitive