Acta Mathematica Vietnamica

, Volume 42, Issue 3, pp 445–454

# Regularity of Powers of Edge Ideals of Some Graphs

Article

## Abstract

Let $$\tilde {C_{n}}$$ be the graph by adding an ear to C n and $$I=I(\tilde {C_{n}})$$ be its edge ideal. In this paper, we prove that $$\operatorname {reg}(I^{s})=2s+\lfloor \frac {n+1}{3}\rfloor -1$$ for all s ≥ 1. Let G be the bicyclic graph C m C n with edge ideal I = I(G); we compute the regularity of I s for all s ≥ 1. In particular, in some cases, we get $$\operatorname {reg}(I^{s})=2s+\lfloor \frac {m}{3}\rfloor +\lfloor \frac {n}{3}\rfloor -1$$ for all s ≥ 2.

## Keywords

Castelnuovo-Mumford regularity Edge ideals Powers of ideals

## Mathematics Subject Classification (2010)

13D02 05E40 05C38

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