  We apply the matrix model of Kapustin, Willett and Yaakov to compute the free
energy of N=3 Chern-Simons matter theories with D_n quivers in the large N
limit. We conjecture a general expression for the free energy that is
explicitly invariant under Seiberg duality and show that it can be interpreted
as a sum over certain graphs known as signed graphs. Through the AdS/CFT
correspondence, this leads to a prediction for the volume of certain tri-Sasaki
Einstein manifolds. We also study the unfolding procedure, which relates these
D_n quivers to A_{2n-5} quivers. Furthermore, we consider the addition of
massive fundamental flavor fields, verifying that integrating these out
decreases the free energy in accordance with the F-theorem.
