ABSTRACT
In this paper, we compute depth and Stanley depth for the quotient ring of the edge ideal associated to a square path on n vertices. We also compute depth and Stanley depth for the quotient ring of the edge ideal associated to a square cycle on n vertices, when n≡0,3,4( mod 5), and give tight bounds when n≡1,2( mod 5). We also prove a conjecture of Herzog presented in [Citation5], for the edge ideals of square paths and square cycles.
2000 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgment
The authors would like to thank the referee for a careful reading of the paper and for valuable comments. The authors would like to thank the referee for a careful reading of the paper and for valuable comments. This research is partially supported by HEC Pakistan.