A generalized Beraha conjecture for non-planar graphs

Understand

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.