The $\circ$ operation and $*$ operation of Cohen-Macaulay bipartite graphs

Yulong Yang; Guangjun Zhu; Yijun Cui; Shiya Duan

The $\circ$ operation and $*$ operation of Cohen-Macaulay bipartite graphs

Commutative Algebra 2023-09-29 v2

Authors: Yulong Yang , Guangjun Zhu , Yijun Cui , Shiya Duan

Abstract

Let $G$ be a finite simple graph with the vertex set $V$ and let $I_G$ be its edge ideal in the polynomial ring $S=\mathbb{K}[x_V]$ . In this paper, we compute the depth and the Castelnuovo--Mumford regularity of $S/I_G$ when $G=G_1\circ G_2$ or $G=G_1* G_2$ is a graph obtained from Cohen-Macaulay bipartite graphs $G_1$ , $G_2$ by $\circ$ operation or $*$ operation, respectively.

Keywords

cohen-macaulay bipartite graph edge ideal depth castelnuovo-mumford regularity graph operation

Cite

@article{arxiv.2309.13568,
  title  = {The $\circ$ operation and $*$ operation of Cohen-Macaulay bipartite graphs},
  author = {Yulong Yang and Guangjun Zhu and Yijun Cui and Shiya Duan},
  journal= {arXiv preprint arXiv:2309.13568},
  year   = {2023}
}

Comments

arXiv admin note: text overlap with arXiv:2308.06010

The $\circ$ operation and $*$ operation of Cohen-Macaulay bipartite graphs

Abstract

Keywords

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