The aim of this paper is to investigate the interplay between the algebraic properties of a skew Poincar´e–Birkhoff–Witt extesion ring A = σ(R)x1, . . . , xn and the graphtheoretic properties of its zero-divisor graph. We are interested in studying the diameter of the zero-divisor graph of skew PBW extension rings. Among other results, we give a complete characterization of the possible diameters of Γ(A) in terms of the diameter of Γ(R).
