Ideal based hypergraph of a commutative ring. Issue 1 (18th March 2022)

• Record Type: Journal Article
• Authors: Amritha, V. C.; Selvakumar, K.
• Is Part Of: AKCE International Journal of Graphs and Combinatorics. Volume 19:Issue 1(2022)
• Page Start: 18
• Page End: 23
• Publication Date: 2022-03-18
• Subjects: Co-maximal ideal graph -- k-maximal ideal hypergraph -- complete -- planar; 05C10 -- 05C65 -- 13A99
• DOI: 10.1080/09728600.2021.2007039
• Languages: English
• ISSNs: 0972-8600

Abstract

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 ) .