The zero-divisor graph of an amalgamated algebra

Let R and S be commutative rings with identity, $$f:R\rightarrow S$$ a ring homomorphism and J an ideal of S. Then the subring $$R\bowtie ^fJ:=\{(r,f(r)+j)\mid r\in R$$ and $$j\in J\}$$ of $$R\times S$$ 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 provide new characterizations for completeness of the zero-divisor graph of amalgamated algebra, as well as, a complete description for the diameter of the zero-divisor graph of amalgamations in the special case of finite rings.