The associated graded algebras of Brauer graph algebras II: infinite representation type

Let $G$ be a Brauer graph and $A$ the associated Brauer graph algebra. Denote by $gr(A)$ the graded algebra associated with the radical filtration of $A$. The question when $gr(A)$ is of finite representation type was answered in [9]. In the present paper, we characterize when $gr(A)$ is domestic in terms of the associated Brauer graph $G$.