The equivalent resistance of the circuit across AB is given by

If V_A > V_B both the junction diodes are forward biased and the given circuit diagram becomes a balanced Wheatstone bridge The equivalent resistance in this case becomes 4Ω , 

If  V_A < V_B the diodes are reverse biased in which case 4Ω, 5Ω and 4Ω are in series, equivalent resistance will be 13Ω.