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Journals / Sinop Üniversitesi Fen Bilimleri Dergisi / 2026 / Cilt: 9 Sayı: 1

Bounds For Spectral Radius and Energy of $PIS$ Graphs

$PIS$ Grafların Spektral Yarıçapı ve Enerjisi İçin Sınırlar

Esra Öztürk Sözen(SİNOP ÜNİVERSİTESİ)0000-0002-2632-2193
Elif Eryaşar(SİNOP ÜNİVERSİTESİ)0000-0002-9852-6662
Pages
26–35
Publication Date
2024-06-29
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AI Summary & Key Takeaways

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

A SageMath code for plotting these graphs is also provided.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Once the spectral radius and energy of a graph structure have been defined, many properties have been studied.
📊
Key Findings & Data:The spectral radius and energy of a graph are related to the eigenvalues of the adjacency matrix of the graph.
💡
Conclusion & Impact:A SageMath code for plotting these graphs is also provided.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Graf enerjisi · asal ideal toplam graf · spektral yarıçap

Abstract

Once the spectral radius and energy of a graph structure have been defined, many properties have been studied. The spectral radius and energy of a graph are related to the eigenvalues of the adjacency matrix of the graph. In this paper, we define an adjacency matrix for a prime ideal sum ($PIS$) graph and then extend the concepts of spectral radius and energy to $PIS$ graphs. Some bound theorems on the energy and spectral radius of $PIS$ graph structures are given. A SageMath code for plotting these graphs is also provided.

Özet

Bir graf yapısının spektral yarıçapı ve enerjisi tanımlandıktan sonra birçok özelliği incelenmiştir. Grafların spektral yarıçapı ve enerjisi komşuluk matrisin özdeğerleriyle ilişkilidir. Bu çalışmada bir asal ideal toplam ($PIS$) graf için bir komşuluk matrisi tanımlanmıştır ve daha sonra spektral yarıçap ve enerji kavramları $PIS$ grafları için genişletilmiştir. $PIS$ graf yapılarının enerjisi ve spektral yarıçapına ilişkin bazı sınır teoremleri verilmiştir. Ayrıca bu grafları çizmek için bir SageMath kodu da sunulmaktadır.

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Cite This Article

Sözen, E. Ö., Eryaşar, E. (2024). Bounds For Spectral Radius and Energy of $PIS$ Graphs. Sinop Üniversitesi Fen Bilimleri Dergisi, Cilt: 9 Sayı: 1, 26–35. https://doi.org/10.33484/sinopfbd.1343041

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