某类图中边理想及其幂的规则性的一些界限

Pub Date : 2024-01-29 DOI:10.1556/012.2023.04298

T. Ashitha, Thangaraj Asir, Do Trong Hoang, M. R. Pournaki

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引用次数: 0

摘要

设𝑛 ≥ 2 为整数。将 {0, ... , 𝑛 - 1} 中的所有元素设为顶点，并定义不同的顶点 𝑥 和 𝑦 为相邻顶点，当且仅当 gcd(𝑥 + 𝑦, 𝑛) ≠ 1 时。本文给出了 .

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Some Bounds for the Regularity of the Edge Ideals and Their Powers in a Certain Class of Graphs

Let 𝑛 ≥ 2 be an integer. The graph is obtained by letting all the elements of {0, … , 𝑛 − 1} to be the vertices and defining distinct vertices 𝑥 and 𝑦 to be adjacent if and only if gcd(𝑥 + 𝑦, 𝑛) ≠ 1. In this paper, we give some bounds for the Castelnuovo–Mumford regularity of the edge ideals and their powers for .

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