  The evaluation of graphs on 2-spheres is a central ingredient of the
Turaev-Viro construction of three-dimensional topological field theories. In
this article, we introduce a class of graphs, called extruded graphs, that is
relevant for the Turaev-Viro construction with general defect configurations
involving defects of various dimensions. We define the evaluation of extruded
graphs and show that it is invariant under a set of moves. This ensures the
computability and uniqueness of our evaluation.
