  We present both analytic and numerical results on the position of the
partition function zeros on the complex magnetic field plane of the $q=2$
(Ising) and $q=3$ states Potts model defined on $\phi^3 $ Feynman diagrams
(thin random graphs). Our analytic results are based on the ideas of
destructive interference of coexisting phases and low temperature expansions.
For the case of the Ising model an argument based on a symmetry of the saddle
point equations leads us to a nonperturbative proof that the Yang-Lee zeros are
located on the unit circle, although no circle theorem is known in this case of
random graphs. For the $q=3$ states Potts model our perturbative results
indicate that the Yang-Lee zeros lie outside the unit circle. Both analytic
results are confirmed by finite lattice numerical calculations.
