2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136968Associated to a finite graph $X$ is its quantum automorphism group $G(X)$. We prove a formula of type $G(X*Y)=G(X)*_wG(Y)$, where $*_w$ is a free wreath product. Then we discuss representation theory of free wreath products, with the conjectural formula $μ(G*_wH)=μ(G)\boxtimesμ(H)$, where $μ$ is the associated spectral measure. This is verified in two situations: one using free probability techniques, the other one using planar algebras.31 pagesQuantum Algebra16W30 (46L37, 46L54)text