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Dergiler / 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
Sayfa
92–109
Yayın Tarihi
2022-10-18
DOI
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We also give some sharp upper bounds for depth and Stanley depth in the general cases.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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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Temel Bulgular & Veri: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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Sonuç & Katkı:We also give some sharp upper bounds for depth and Stanley depth in the general cases.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (19)

  1. C. Bir, D.M. Howard, M.T. Keller, W.T. Trotter and S.J. Young, Interval partitions and Stanley depth, J. Combin. Theory Ser. A, 117, 475–482, 2010
  2. M. Cimpoeaş, Several inequalities regarding Stanley depth, Romanian Journal of Math. and Computer Science, 2, 28–40, 2012
  3. M. Cimpoeaş, Stanley depth of squarefree Veronese ideals, An. St. Univ. Ovidius Constanta, 21 (3), 67–71, 2013
  4. M. Cimpoeaş, On the Stanley depth of edge ideals of line and cyclic graphs, Romanian Journal of Math. and Computer Science, 5 (1), 70–75, 2015
  5. CoCoATeam, CoCoA: a system for doing Computations in Commutative Algebra, available at
  6. A.M. Duval, B. Goeckner, C.J. Klivans and J.L. Martine, A non-partitionable Cohen- Macaulay simplicial complex, Adv. Math. 299, 381–395, 2016
  7. S.A.S. Fakhari, On the Stanley Depth of Powers of Monomial Ideals, Mathematics, 7, 607, 2019
  8. L. Fouli and S. Morey, A lower bound for depths of powers of edge ideals, J. Algebraic Combin. 42 (3), 829–848, 2015
  9. R. Hammack, W. Imrich and S. Klavar, Handbook of Product Graphs, Second Edition, CRC Press, Boca Raton, FL, 2011
  10. J. Herzog, A survey on Stanley depth, In Monomial ideals, computations and applications, Lecture Notes in Math. 2083, Springer, Heidelberg, 3–45, 2013
  11. J. Herzog, M. Vladoiu and X. Zheng, How to compute the Stanley depth of a monomial ideal, J. Algebra, 322 (9), 3151–3169, 2009
  12. Z. Iqbal and M. Ishaq, Depth and Stanley depth of edge ideals associated to some line graphs, AIMS Mathematics, 4 (3), 686–698, 2019
  13. Z. Iqbal and M. Ishaq, Depth and Stanley depth of edge ideals of powers of paths and cycles, An. Şt. Univ. Ovidius Constana, 27 (3), 113–135, 2019
  14. Z. Iqbal, M. Ishaq and M. Aamir, Depth and Stanley depth of edge ideals of square paths and square cycles, Comm. Algebra, 46 (3), 1188–1198, 2018
  15. M. Ishaq, Upper bounds for the Stanley depth, Comm. Algebra, 40 (1), 87–97, 2012
  16. M. Ishaq, Values and bounds for the Stanley depth, Carpathian J. Math. 27 (2), 217–224, 2011
  17. M. Ishaq and M.I. Qureshi, Upper and lower bounds for the Stanley depth of certain classes of monomial ideals and their residue class rings, Comm. Algebra, 41 (3), 1107–1116, 2013
  18. M.T. Keller and S.J. Young, Combinatorial reductions for the Stanley depth of I and S/I, Electron. J. Comb. 24 (3), #P3.48, 2017
  19. M.T. Keller, Y. Shen, N. Streib and S.J. Young, On the Stanley depth of squarefree veronese ideals, J. Alge