  A colored Gaussian graphical model is a linear concentration model in which
equalities among the concentrations are specified by a coloring of an
underlying graph. The model is called RCOP if this coloring is given by the
edge and vertex orbits of a subgroup of the automorphism group of the graph. We
show that RCOP Gaussian graphical models on block graphs are toric in the space
of covariance matrices and we describe Markov bases for them. To this end, we
learn more about the combinatorial structure of these models and their
connection with Jordan algebras.
