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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2021 / Volume: 70 Issue: 2

A graph associated to a commutative semiring

Shahabaddin Ebrahimi Atani(University of Guilan)0000-0003-0568-9452
Mehdi Khoramdel(Universty Of Guilan)0000-0003-0663-0356
Saboura Dolatı Pısh Hesarı(University of Guilan)0000-0001-8830-636X
Mahsa Nıkmard Rostam Alıpour(University Of Guilan)0000-0003-3264-7936
Pages
—
Publication Date
2021-12-31
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AI Summary & Key Takeaways

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

Moreover, we characterize the planarity, chromatic number, clique number and independence number of G H ( R ) GH(R) .

📌 3 Key Takeaways

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Objective & Hypothesis:Let R R be a commutative finite semiring with nonzero identity and H H be an arbitrary multiplicatively closed subset R R .
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Key Findings & Data:The generalized identity-summand graph of R R is the (simple) graph G H ( R ) GH(R) with all elements of R R as the vertices, and two distinct vertices x x and y y are adjacent if and only if x + y ∈ H x+y∈H .
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Conclusion & Impact:Moreover, we characterize the planarity, chromatic number, clique number and independence number of G H ( R ) GH(R) .
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:I-semiring · planar graphs · clique number

Abstract

Let R R be a commutative finite semiring with nonzero identity and H H be an arbitrary multiplicatively closed subset R R . The generalized identity-summand graph of R R is the (simple) graph G H ( R ) GH(R) with all elements of R R as the vertices, and two distinct vertices x x and y y are adjacent if and only if x + y ∈ H x+y∈H . In this paper, we study some basic properties of G H ( R ) GH(R) . Moreover, we characterize the planarity, chromatic number, clique number and independence number of G H ( R ) GH(R) .

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Cite This Article

Atani, S. E., Khoramdel, M., Hesarı, S. D. P., Alıpour, M. N. R. (2021). A graph associated to a commutative semiring. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 70 Issue: 2. https://doi.org/10.31801/cfsuasmas.783398

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