@article{d192b0296e3c40749742191841ce40d1,
title = "Very well-covered graphs and local cohomology of their residue rings by the edge ideals",
abstract = "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.",
keywords = "CM property, Depth, Edge ideal, Height, Independence complex, Local cohomology, Regularity, Simplicial complex, Stanley–Reisner ideal, Very well-covered graph",
author = "K. Kimura and Pournaki, {M. R.} and N. Terai and S. Yassemi",
note = "Funding Information: The research of K. Kimura was in part supported by a grant from The Japan Society for the Promotion of Science (JSPS Grant-in Aid for Young Scientists (B) – Ref. 15K17507 ). The research of M.R. Pournaki was in part supported by a grant from The World Academy of Sciences (TWAS–UNESCO Associateship – Ref. 3240295905 ). The research of N. Terai was in part supported by a grant from The Japan Society for the Promotion of Science (JSPS Grant-in-Aid for Scientific Research (C) – Ref. 18K03244 ). Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",
year = "2022",
month = sep,
day = "15",
doi = "10.1016/j.jalgebra.2022.04.021",
language = "English",
volume = "606",
pages = "1--18",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
}