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

Abstract

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 .