On free products of graphs

Max Carter, Stephan Tornier, George A. Willis

Published 2020-02-25Version 1

We define a free product of connected simple graphs that is equivalent to several existing definitions when the graphs are vertex-transitive but differs otherwise. The new definition is designed for the automorphism group of the free product to be as large as possible, and we give sufficient criteria for it to be non-discrete. Finally, we transfer Tits' classification of automorphisms of trees and simplicity criterion to free products of graphs.