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

Let R be a commutative ring with identity and let I be an ideal of R. Let RbowtieI be the subring of R×R consisting of the elements (r,r+i) for rset membership, variantR and iset membership, variantI. We study the diameter and girth of the zero-divisor graph of the ring RbowtieI.