The diameter of the zero-divisor graph of an amalgamated algebra

Let R and S be commutative rings with unity, f : R -> S a ring homomorphism and J an ideal of S. Then the subring R (sic)(f) J := {(r, f (r) + j) | r is an element of R and j is an element of J} of R x S is called the amalgamation of R with S along J with respect to f. In this paper we generalize and improve recent results on the computation of the diameter of the zero-divisor graph of amalgamated algebras and obtain new results. In particular, we characterize the diameter of the zero-divisor graph of amalgamated duplication.