The diameter of annihilator ideal graph of ℤn

Let x ∈ ℤn and AI(x) = {r ∈ ℤn : rx ∈ I}. The annihilator ideal graph of ℤn, denoted by AGI (ℤn) is the undirected graph with vertex set V(AGI(ℤn))={ x∈ℤn\I:xy∈I,y∉I }, and two distinct vertices x and y are adjacent if and only if AI(xy) ≠ AI(x)∪AI(y). In this paper, we study the diameter of annihilator ideal graph of ℤn, where ℤn is a commutative ring of integers modulo n.