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

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