Narrow Results

In this paper, we study the Castelnuovo–Mumford regularity of powers of edge ideals of product of graphs. We find new upper bounds for $reg(I{(G\ast H)}^s)$ for various classes of graphs $G$ and $H$, where $G\ast H$ denotes the product of $G$ and $H$, and $I(G\ast H)$ denote the corresponding edge ideal. Using this result, we explicitly compute $reg(I{(G\ast H)}^s)$ for several classes of graphs $G$ and $H$. In particular, we also explicitly compute the regularity of powers of wheel graphs.