On knot groups acting on trees

A finitely generated group $G$ acting on a tree with infinite cyclic edge and vertex stabilizers is called a generalized Baumslag–Solitar group ($GBS$ group). We prove that a 1-knot group $G$ is $GBS$ group iff $G$ is a torus-knot group and describe all n-knot GBS groups for $n⩾3$.