Automorphism groups of trees and graphs

This lecture covers the concept of automorphisms of graphs, focusing on the automorphism groups of trees and graphs, Cayley-Abels graphs, and quasi-isometry. The lecture explains the structure of graphs, including vertex and edge sets, and the properties of simple and locally finite graphs. It discusses the definition of automorphism groups, the permutation topology, and the action of a group on a graph. The lecture also presents two constructions with compact open subgroups and explores the quasi-isometry of Cayley-Abels graphs. Examples and theorems related to Cayley-Abels graphs and quasi-isometry are provided, along with proofs and exercises.