Ideal based hypergraph of a commutative ring. Issue 1 (18th March 2022) - Amritha, V. C.; Selvakumar, K.
Abstract: Let R be a commutative ring and k an integer strictly greater than 2. The k - maximal ideal hypergraph H Γ k ( R ) to R with vertex set C ( R, k ), the set of all k -maximal ideals in R and for distinct ideals I 1, I 2, I 3, …, I k in C ( R, k ), the set { I 1, I 2, …, I k } is an edge of H Γ k ( R ) if and only if ∑ i = 1 k I i = R and the sum of any ( k − 1 ) elements of { I 1, I 2, …, I k } is not equal to R . This article analyses some basic properties of H Γ k ( R ) and we have shown that H Γ 3 ( R ) is connected with diameter at most 2. Also, we discuss about the planarity and isomorphism of H Γ k ( R ) .