科恩-麦考莱双方形图的◦运算和＊运算

Pub Date : 2024-07-21 DOI:10.21136/cmj.2024.0438-23

Yulong Yang, Guangjun Zhu, Yijun Cui, Shiya Duan

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引用次数: 0

摘要

设 G 是顶点集为 V 的有限简单图，设 IG 是它在（S=\mathbb{K}[V]\）多项式环中的边理想。当 G = G1 ◦ G2 或 G = G1 * G2 分别是由科恩-马科莱双向图 G1、G2 通过 ◦ 操作或 * 操作得到的图时，我们计算 S/IG 的深度和卡斯特诺沃-蒙福德正则性。

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The ◦ operation and * operation of Cohen-Macaulay bipartite graphs

Let G be a finite simple graph with the vertex set V and let I_G be its edge ideal in the polynomial ring \(S=\mathbb{K}[V]\). We compute the depth and the Castelnuovo-Mumford regularity of S/I_G when G = G₁ ◦ G₂ or G = G₁ * G₂ is a graph obtained from Cohen-Macaulay bipartite graphs G₁, G₂ by the ◦ operation or * operation, respectively.

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