Abstract: Given a finite graph $\Gamma$ with vertices labelled by groups $G_1, \dots, G_n$, the graph product is a neat construction that interpolates between the free product $G_1 \ast G_2 \ast \cdots \ast G_n$ and the direct product $G_1 \times G_2 \times \cdots \times G_n$. Right-angled Coxeter groups and right-angled Artin groups are well-studied examples of groups naturally represented as graph products of groups. The automorphism groups of graph products of groups are interesting for their relationships to other well-studied groups of automorphisms, and for the things that remain unknown about them. We give an overview of some results.
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