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 H-3 (R; I), is a hypergraph whose vertices are {x(1) is an element of R\I\ x(1)x(2)x(3) is an element of I for some x(2); x(3) is an element of R\I such that x(1) x(2) is not an element of I; x(1) x(3) is not an element of I and x(2) x(3) is not an element of I} where distinct vertices x(1); x(2) and x(3) are adjacent if and only if x(1)x(2)x(3) is an element of I, x(1)x(2) is an element of I, x(1)x(3) is not an element of I and x(2) x(3) is not an element of 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.