Line graph embedding of co-intersection graph of ideals of commutative rings
Year: 2025
Type: article
Abstract: This research paper focuses on the co-intersection graph of a commutative ring S. The co-intersection graph of S denoted by Ω(S) is a simple graph with vertices that are non-trivial ideals of S, and two distinct vertices I and J are adjacent if and only if I+J≠S. The primary goal of this study is to characterize Artinian commutative rings S, and determining whether their associated co-intersection graph Ω(S) forms a line graph and identifying instances where it becomes the complement of a line graph. Additionally, the article investigates the planarity and outerplanarity of the line graph of the co-intersection graph Ω(S). Finally, the research identifies the genus one of this line graph of co-intersection graph of ideals of a commutative ring.
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,226
OpenAlex ID: W4413104300