3-zero-divisor hypergraph regarding an ideal

Abstract

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 H3(R, I), is a hypergraph whose vertices are {x1 ∈ R\I|x1x2x3 ∈ I for some x2, x3 ∈ R\I such that x1x2 ∉ I, x1x3 ∉ I and x2x3 ∉ I} where distinct vertices x1, x2 and x3 are adjacent if and only if x1x2x3 ∈ I, x1x2 ∉ I, x1x3 ∉ I and x2x3 ∉ I. These vertices consist of an hyperedge in H3(R, I). In this study, we investigate some properties of H3(R, I). Also, we compute a lower bound of diameter of H3(R, I) and notice that it is connected.