In this paper we give a recursive formula for the conjugacy growth series of a graph product in terms of the conjugacy growth and standard growth series of subgraph products. We also show that the conjugacy and standard growth rates in a graph product are equal provided that this property holds for each vertex group. All results are obtained for the standard generating set consisting of the union of generating sets of the vertex groups.
Cite this article
Laura Ciobanu, Susan Hermiller, Valentin Mercier, Formal conjugacy growth in graph products I. Groups Geom. Dyn. 17 (2023), no. 2, pp. 427–457DOI 10.4171/GGD/704