Regularity of powers of edge ideal of whiskered cycles

Mahdieh Moghimian, Seyed Amin Seyed Fakhari, Siamak Yassemi

Let $G=W(C_n)$ be a whiskered cycle graph with edge ideal $I=I(G)$. We prove that for every $s\ge 1$, the equality $\mathrm{reg}(I^s)=2s+\lceil \frac{n-1}{2}\rceil -1$ holds.