Associated primes of powers of cover ideals under graph operations

Abstract

An ideal I in a commutative Noetherian ring R has the strong persistence property if $(I^{t+1}{:}_{R}I)=I^t$ for all positive integers t. In this article, we focus on how some graph operations affect the strong persistence property of the cover ideals. As applications, we show that the cover ideals of some imperfect graphs satisfy the strong persistence property.

Keywords:

• Cycles
• Helm graphs
• wheel graphs
• cover ideals
• associated primes

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 05C25
• 05C38
• 05E40
• 13P25

Acknowledgements

The authors are deeply grateful to anonymous referee for careful reading of the manuscript. Moreover, the authors would like to thank Professor Adam Van Tuyl for his valuable suggestions which led to some improvements in the quality of this article.