Year: 2026
Type: article
Abstract: This research article examines the co-intersection graph of a commutative ring š®. The co-intersection graph Ī©(š®) is defined as a simple graph where the vertices correspond to the non-trivial ideals of š®, and two distinct vertices I and J are adjacent if and only if I+Jā š®. In this study, we first classify the Artinian rings š® for which Ī©(š®) is isomorphic to certain basic graphs, such as a unicycle, a split graph, or a threshold graph. Subsequently, we investigate the genus of Ī©(š®) and identify the rings š® for which Ī©(š®) represents a double-toroidal graph. Furthermore, we analyze the crosscap of Ī©(š®) and determine the rings š® for which Ī©(š®) corresponds to the projective plane or the Klein bottle. Lastly, we compute the book thickness of Ī©(š®) for cases where the genus is at most one.
Source: Mathematics
DOI: 10.3390/math14091404
Authors: Turki Alsuraiheed, Junaid Nisar
Institutions: King Saud University, Symbiosis International University
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Funder: King Saud University
Award: G1564389638
OpenAlex ID: W7155212905
FWCI:
Cites:
Cited by:
Related to: