Zero-divisor graphs of amalgamated duplication of a ring along an ideal

Abstract Let R be a commutative ring with identity and let I be an ideal of R . Let R ⋈ I be the subring of R × R consisting of the elements ( r , r + i ) for r ∈ R and i ∈ I . We study the diameter and girth of the zero-divisor graph of the ring R ⋈ I .