  We consider a graph polynomial \xi(G;x,y,z) introduced by Averbouch, Godlin,
and Makowsky (2007). This graph polynomial simultaneously generalizes the Tutte
polynomial as well as a bivariate chromatic polynomial defined by Dohmen,
Poenitz and Tittmann (2003). We derive an identity which relates the graph
polynomial of a thicked graph (i.e. a graph with each edge replaced by k copies
of it) to the graph polynomial of the original graph. As a consequence, we
observe that at every point (x,y,z), except for points lying within some set of
dimension 2, evaluating \xi is #P-hard.
