  We obtain in a closed form the 1/N^2 contribution to the free energy of the
two Hermitian N\times N random matrix model with non symmetric quartic
potential. From this result, we calculate numerically the Yang-Lee zeros of the
2D Ising model on dynamical random graphs with the topology of a torus up to
n=16 vertices. They are found to be located on the unit circle on the complex
fugacity plane. In order to include contributions of even higher topologies we
calculated analytically the nonperturbative (sum over all genus) partition
function of the model Z_n = \sum_{h=0}^{\infty} \frac{Z_n^{(h)}}{N^{2h}} for
the special cases of N=1,2 and graphs with n\le 20 vertices. Once again the
Yang-Lee zeros are shown numerically to lie on the unit circle on the complex
fugacity plane. Our results thus generalize previous numerical results on
random graphs by going beyond the planar approximation and strongly indicate
that there might be a generalization of the Lee-Yang circle theorem for
dynamical random graphs.
