On the Depth of Generalized Binomial Edge Ideals

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-26 DOI:10.1007/s00009-024-02685-2

J. Anuvinda, Ranjana Mehta, Kamalesh Saha

引用次数: 0

Abstract

This research focuses on analyzing the depth of generalized binomial edge ideals. We extend the notion of d-compatible map and use it to give a combinatorial lower bound for the depth of generalized binomial edge ideals. Subsequently, we determine an upper bound for the depth of generalized binomial edge ideals in terms of the vertex-connectivity of graphs. We demonstrate that the difference between the upper and lower bounds can be arbitrarily large, even in cases when one of the bounds is sharp. In addition, we calculate the depth of generalized binomial edge ideals of certain classes of graphs, including cycles and graphs with Cohen-Macaulay binomial edge ideals.

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论广义二项式边理想的深度

本研究主要分析广义二叉边理想的深度。我们扩展了 d 兼容映射的概念，并利用它给出了广义二项式边理想深度的组合下限。随后，我们根据图的顶点连接性确定了广义二项式边理想的深度上限。我们证明，上界和下界之间的差异可以任意大，即使其中一个界限是尖锐的。此外，我们还计算了某些类别图的广义二项式边理想深度，包括循环图和具有科恩-麦考莱二项式边理想的图。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.