Regularity of Powers of Unicyclic Graphs

Abstract

Let $G$ be a finite simple graph and $I(G)$ denote the corresponding edge ideal. In this paper we prove that if $G$ is a unicyclic graph then for all $s\ge 1$ the regularity of $I(G{)}^s$ is exactly $2s+\text{reg}(I(G))-2$. We also characterize the unicyclic graphs with regularity $\nu (G)+1$ and $\nu (G)+2$, where $\nu (G)$ denotes the induced matching number of $G$.

References in corpus (2)

• Betti Numbers of Graph Ideals
• Stability of Depths of Powers of Edge Ideals

Cited by in corpus (2)

• Symbolic powers of edge ideals of graphs
• Regularity of Powers of edge ideal of very well-covered graphs