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Very well-covered graphs and local cohomology of their residue rings by the edge ideals

Kimura, K ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1016/j.jalgebra.2022.04.021
  3. Publisher: Academic Press Inc , 2022
  4. Abstract:
  5. In this paper, we deal with very well-covered graphs. We first describe the structure of these kinds of graphs based on the structure of Cohen–Macaulay very well-covered graphs. As an application, we analyze the structure of local cohomology of the residue rings by the edge ideals of very well-covered graphs. Also, we give different formulas of regularity and depth of these rings from known ones and we finally treat the CMt property. © 2022 Elsevier Inc
  6. Keywords:
  7. CMt property ; Depth ; Edge ideal ; Height ; Independence complex ; Local cohomology ; Regularity ; Simplicial complex ; Stanley–Reisner ideal ; Very well-covered graph
  8. Source: Journal of Algebra ; Volume 606 , 2022 , Pages 1-18 ; 00218693 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0021869322001971