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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Cilt: 68 - Sayı: 1

Intersection graphs of co-ideals of semirings

S. Ebrahimi ATANİ
Saboura Dolati PİSHHESARİ
Mehdi KHORAMDEL
Zahra Ebrahimi SARVANDİ
Pages
840–851
Publication Date
2019-02-01
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The basic properties and possible structures of this graph are studied and the interplay between the algebraic properties of R and the graph-theoretic structure of G(R) is investigated.

📌 3 Key Takeaways

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Objective & Hypothesis:Let R be a semiring with identity.
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Key Findings & Data:The vertices of G(R) are non-trivial co-ideals of R, and two distinct vertices I and J are adjacent if and only if I∩J≠{1}.
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Conclusion & Impact:The basic properties and possible structures of this graph are studied and the interplay between the algebraic properties of R and the graph-theoretic structure of G(R) is investigated.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Co-ideal · intersection graph · I-semiring

Abstract

Let R be a semiring with identity. In this paper, we introduce the intersection graph of co-ideals, denoted by G(R). The vertices of G(R) are non-trivial co-ideals of R, and two distinct vertices I and J are adjacent if and only if I∩J≠{1}. The basic properties and possible structures of this graph are studied and the interplay between the algebraic properties of R and the graph-theoretic structure of G(R) is investigated.

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Cite This Article

ATANİ, S. E., PİSHHESARİ, S. D., KHORAMDEL, M., SARVANDİ, Z. E. (2019). Intersection graphs of co-ideals of semirings. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 68 - Sayı: 1, 840–851. https://ajindex.com/articles/747101

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References (2)

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