r-well covered graphs of L (+) N

Al-Labadi, Manal; Almuhur, Eman; Khalil, Shuker

doi:10.47974/JDMSC-2321

Open Access Research Article

r-well covered graphs of L (+) N

Manal Al-Labadimanal.allabadi@uop.edu.joDepartment of MathematicsFaculty of Arts and SciencesUniversity of PetraAmman, JordanView full profile → , Eman Almuhuralmuhur@asu.edu.joDepartment of MathematicsFaculty of ScienceApplied Science Private UniversityAmman, JordanView full profile → , ^*Shuker KhalilCorresponding authorshuker.khalil@uobasrah.edu.iqDepartment of MathematicsCollege of ScienceUniversity of BasrahBasrah, IraqView full profile →

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pp. 1307–1312Vol. 29Issue 3March 2026DOI: 10.47974/JDMSC-2321 Crossmark XML

Received:: 02 Jun 2025
Published Online:: 09 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-2321
Pages:: 1307–1312

Abstract

This paper presents an efficiently covered property of the zero-divisor graph of L (+) N, with L a commutative ring with the identity element and N an L−module. we present a complete characterization of when Γ (L (+) N) is well covered in terms of the annihilator structure of N. Moreover, new concept is introduced its r−well covered graphs: as far as a well-covered graph has all maximal independent sets of size r. They can further prove that if L is an integral domain, ann(N) = 0 and if the graph Γ (L (+) N) is well covered in the sense of (|N|− 1) −well covered. All this goes to show that at least a meaningful link must exist between the algebraic structural condition of idealization rings and the corresponding graph-theoretic properties of their associated zero-divisor graphs: something quite different from the former studies on clique numbers and independence numbers in these structures.

Keywords

Mathematical modeling Ordinary differential equations A duopoly economy Market share

Subject Classifications

Primary 05CxxSecondary 05C38

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