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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 1

Depth and Stanley depth of the edge ideals of the strong product of some graphs

Zahid Iqbal
Muhammad Ishaq
Muhammad Ahsan Binyamin
Pages
92–109
Publication Date
2022-10-18
DOI
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AI Summary & Key Takeaways

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

We also give some sharp upper bounds for depth and Stanley depth in the general cases.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we study depth and Stanley depth of the edge ideals and quotient rings of the edge ideals, associated with classes of graphs obtained by the strong product of two graphs.
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Key Findings & Data:We consider the cases when either both graphs are arbitrary paths or one is an arbitrary path and the other is an arbitrary cycle.
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Conclusion & Impact:We also give some sharp upper bounds for depth and Stanley depth in the general cases.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Depth · Stanley depth · Stanley decomposition

Abstract

In this paper, we study depth and Stanley depth of the edge ideals and quotient rings of the edge ideals, associated with classes of graphs obtained by the strong product of two graphs. We consider the cases when either both graphs are arbitrary paths or one is an arbitrary path and the other is an arbitrary cycle. We give exact formula for values of depth and Stanley depth for some subclasses. We also give some sharp upper bounds for depth and Stanley depth in the general cases.

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Cite This Article

Iqbal, Z., Ishaq, M., Binyamin, M. A. (2022). Depth and Stanley depth of the edge ideals of the strong product of some graphs. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 1, 92–109. https://ajindex.com/articles/529479

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