  Let $\k$ be a field and $Q$ a minimal Hopf quiver, i.e., a cyclic quiver or
the infinite linear quiver, and let $\rep^{ln}(Q)$ denote the category of
locally nilpotent finite dimensional $\k$-representations of $Q.$ The category
$\rep^{ln}(Q)$ has natural tensor structures induced from graded Hopf
structures on the path coalgebra $\k Q.$ Tensor categories of the form
$\rep^{ln} (Q)$ are an interesting class of tame hereditary pointed tensor
categories which are not finite. The aim of this paper is to compute the
Clebsch-Gordan formulae and Green rings of such tensor categories.
