  We study the partition function Z_{G(nk,k)}(Q,v) of the Q-state Potts model
on the family of (non-planar) generalized Petersen graphs G(nk,k). We study its
zeros in the plane (Q,v) for 1<= k <= 7. We also consider two specializations
of Z_{G(nk,k)}, namely the chromatic polynomial P_{G(nk,k)}(Q) (corresponding
to v=-1), and the flow polynomial Phi_{G(nk,k)}(Q) (corresponding to v=-Q). In
these two cases, we study their zeros in the complex Q-plane for 1 <= k <= 7.
We pay special attention to the accumulation loci of the corresponding zeros
when n -> infinity. We observe that the Berker-Kadanoff phase that is present
in two-dimensional Potts models, also exists for non-planar recursive graphs.
Their qualitative features are the same; but the main difference is that the
role played by the Beraha numbers for planar graphs is now played by the
non-negative integers for non-planar graphs. At these integer values of Q,
there are massive eigenvalue cancellations, in the same way as the eigenvalue
cancellations that happen at the Beraha numbers for planar graphs.
