Regularity of Initial Ideal of Binomial Edge Ideals in Degree 2 and Their Powers

Abstract

In this paper, we study the Castelnuovo-Mumford regularity of the initial ideal of binomial edge ideals in degree 2 ([in<(JG)]2), and their powers for some classes of graphs. Also, we obtain a lower bound for the regularity of powers of binomial edge ideal associated to complete bipartite graphs.