Lethbridge Number Theory and Combinatorics Seminar: Gabriel Verret

  • Date: 11/28/2016
Gabriel Verret, University of Auckland, New Zealand

University of Lethbridge


Vertex-primitive digraphs having vertices with almost equal neighbourhoods


A permutation group G on X is transitive if for every x and y in X, there exists g in G mapping x to y. The group G is called primitive if, in addition, it preserves no nontrivial partition of X. Let Gamma be a vertex-primitive digraph, that is, its automorphism group acts primitively on its vertex-set. It is not hard to see that, in this case, Gamma cannot have two distinct vertices with equal neighbourhoods, unless Gamma is in some sense trivial. I will discuss some recent results about the case when Gamma has two vertices with “almost” equal neighbourhoods, and how these results were used to answer a question of Araújo and Cameron about synchronising groups. (This is joint work with Pablo Spiga.)

Other Information: 

Location: C756 University Hall
Web page: http://www.cs.uleth.ca/~nathanng/ntcoseminar/