On the Depth of Independence Complexes

Abstract

Let G be a graph and I G be its edge ideal so we call Stanley-Reisner ring of G . The depth of a ring is a well-studied and important algebraic invariant in commutative algebra. In this paper we give some results on the depth of Stanley- Reisner rings of graphs and simplicial complexes. By depth Lemma we reduce the computing depth of a codismantlable graph into its induced subgraphs.