### How vertex stabilizers grow?

Algebra Seminar

21st April 2021, 2:30 pm – 3:30 pm

Online, Zoom

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.

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