---
abstract: 'The index of a graded ideal measures the number of linear steps in the graded minimal free resolution of the ideal. In this paper we study the index of powers and squarefree powers of edge ideals. Our results indicate that the index as a function of the power of an edge ideal $I$ is strictly increasing if $I$ has linear relations. Examples show that this need not to be the case for monomial ideals generated in degree greater than two.'
address:
- 'Mina Bigdeli, Faculty of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Gava zang, 45195-1159 Zanjan 45137-66731 Iran'
- 'Jürgen Herzog, Fachbereich Mathematik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany'
- 'Rashid Zaare-Nahandi, Faculty of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Gava zang, 45195-1159 Zanjan 45137-66731 Iran'
author:
- 'Mina Bigdeli, Jürgen Herzog and Rashid Zaare-Nahandi'
title: On the index of powers of edge ideals
---

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Introduction {#introduction .unnumbered}
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In recent years the study of algebraic and homological properties of powers of ideals has been one of the main subjects of research in Commutative Algebra. Generally speaking many of those properties, like for example depth, projective dimension or regularity stabilize 