  We study systems of linear and semilinear mappings considering them as
representations of a directed graph $G$ with full and dashed arrows: a
representation of $G$ is given by assigning to each vertex a complex vector
space, to each full arrow a linear mapping, and to each dashed arrow a
semilinear mapping of the corresponding vector spaces. We extend to such
representations the classical theorems by Gabriel about quivers of finite type
and by Nazarova, Donovan, and Freislich about quivers of tame types.
