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Let Cn~$\tilde {C_{n}}$ be the graph by adding an ear to Cn and I=I(Cn~)$I=I(\tilde {C_{n}})$ be its edge ideal. In this paper, we prove that reg(Is)=2s+⌊n+13⌋−1$\operatorname {reg}(I^{s})=2s+\lfloor \frac {n+1}{3}\rfloor -1$… Click to show full abstract
Let Cn~$\tilde {C_{n}}$ be the graph by adding an ear to Cn and I=I(Cn~)$I=I(\tilde {C_{n}})$ be its edge ideal. In this paper, we prove that reg(Is)=2s+⌊n+13⌋−1$\operatorname {reg}(I^{s})=2s+\lfloor \frac {n+1}{3}\rfloor -1$ for all s ≥ 1. Let G be the bicyclic graph Cm ⊔ Cn with edge ideal I = I(G); we compute the regularity of Is for all s ≥ 1. In particular, in some cases, we get reg(Is)=2s+⌊m3⌋+⌊n3⌋−1$\operatorname {reg}(I^{s})=2s+\lfloor \frac {m}{3}\rfloor +\lfloor \frac {n}{3}\rfloor -1$ for all s ≥ 2.
Journal Title: Acta Mathematica Vietnamica
Year Published: 2017
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