  In this paper we give an algorithm for computing the conjugacy growth series
for a right-angled Artin group, based on a natural language of minimal length
conjugacy representatives. In addition, we provide a further language of unique
conjugacy geodesic representatives of the conjugacy classes for a graph product
of groups. The conjugacy representatives and growth series here provide an
alternate viewpoint, and are more amenable to computational experiments
compared to those in our previous paper.
  Examples of applications of this algorithm for right-angled Artin groups are
provided, as well as computations of conjugacy geodesic growth growth series
with respect to the standard generating sets.
