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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 50 Issue: 1

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

Zahid Iqbal(National University of Sciences and Technology)0000-0003-1549-3584
Muhammad Ishaq(National University of Sciences and Technology)0000-0002-5479-2192
Muhammad Ahsan Binyamin(Government College University Faisalabad)0000-0003-0717-7557
Pages
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Publication Date
2021-02-04
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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. (2021). Depth and Stanley depth of the edge ideals of the strong product of some graphs. Hacettepe Journal of Mathematics and Statistics, Volume: 50 Issue: 1. https://doi.org/10.15672/hujms.638033

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