  We consider multivariate centered Gaussian models for the random vector
$(Z^1,\ldots, Z^p)$, whose conditional structure is described by a homogeneous
graph and which is invariant under the action of a permutation subgroup. The
following paper concerns with model selection within colored graphical Gaussian
models, when the underlying conditional dependency graph is known. We derive an
analytic expression of the normalizing constant of the Diaconis-Ylvisaker
conjugate prior for the precision parameter and perform Bayesian model
selection in the class of graphical Gaussian models invariant by the action of
a permutation subgroup. We illustrate our results with a toy example of
dimension $5$.
