Regularity of symbolic powers of edge ideals of unicyclic graphs

Abstract

Let $G$ be a unicyclic graph with edge ideal $I(G)$. For any integer $s\geq 1$, we denote the $s$-th symbolic power of $I(G)$ by $I(G)^{(s)}$. It is shown that ${\rm reg}(I(G)^{(s)})={\rm reg}(I(G)^s)$, for every $s\geq 1$.