Computing the Dijkgraaf-Witten invariants of arborescent links

The main purpose of this article is to develop a method to compute the untwisted Dijkgraaf-Witten invariant of the complement of any arborescent link. As an application, for Montesinos knots we derive a closed formula for the number of $n$-colorings when $n$ is odd, by partially compute the DW invariant associated to the dihedral group $D_{n}$.