On directed zero-divisor graphs of Ore extensions over reversible rings

For an associative ring R, the directed zero-divisor graph of R is the graph 􀀀(R) such that the vertices of 􀀀(R) are all the nonzero zero-divisors of R and x ! y is an edge between distinct vertices x and y if and only if xy = 0. Our goal in this note is to give a characterization of the possible of diam(􀀀(R[x; ; ])) in terms of diam(􀀀(R)), when the base ring R is reversible and also have the ( ; )-compatible property