  We prove that the mapping torus of a graph immersion has a word-hyperbolic
fundamental group if and only if the corresponding endomorphism does not
produce Baumslag-Solitar subgroups. Due to a result by Reynolds, this theorem
applies to all injective endomorphisms of $F_2$ and nonsurjective fully
irreducible endomorphisms of $F_n$. We also give a framework for extending the
theorem to all injective endomorphisms of $F_n$.
