Pablo Spiga

How vertex stabilizers grow?

In this talk we are interested in graphs having the property that, for any two vertices v and w, there exists an automorphism of the graph mapping v to w. Graphs of this type are rather symmetric and are called vertex transitive. We will see that the cardinality of the stabilizer of a vertex (that is, the cardinality of the set of automorphisms fixing a given vertex) is a natural parameter for measuring how symmetric a given graph is.

Most of the results that we present in this talk show nature, with respect to symmetries, is rather meagre. Namely, we describe a peculiar dichotomy: either the graphs are not very symmetric or the graphs are part of a well-understood and easy to describe family.