3-zero-divisor hypergraph regarding an ideal

Let R be a commutative ring and I be a proper ideal of R. The 3-zero divisor hypergraph regarding an ideal I, denoted by H
₃
(R, I), is a hypergraph whose vertices are {x
₁
∈ R\I|x
₁
x
₂
x
₃
∈ I for some x
₂
, x
₃
∈ R\I such that x
₁
x
₂
∉ I, x
₁
x
₃
∉ I and x
₂
x
₃
∉ I} where distinct vertices x
₁
, x
₂
and x
₃
are adjacent if and only if x
₁
x
₂
x
₃
∈ I, x
₁
x
₂
∉ I, x
₁
x
₃
∉ I and x
₂
x
₃
∉ I. These vertices consist of an hyperedge in H
₃
(R, I). In this study, we investigate some properties of H
₃
(R, I). Also, we compute a lower bound of diameter of H
₃
(R, I) and notice that it is connected.