Regularity of powers of d-sequence (parity) binomial edge ideals of unicycle graphs

Abstract

We classify all unicycle graphs whose edge-binomials form a d-sequence, particularly linear type binomial edge ideals. We also classify unicycle graphs whose parity edge-binomials form a d-sequence. We study the regularity of powers of (parity) binomial edge ideals of unicycle graphs generated by d-sequence (parity) edge-binomials.

Keywords:

• Binomial edge ideal
• d-sequence
• parity binomial edge ideal
• regularity

2020 Mathematics Subject Classification:

• 13F65
• 05E40
• 13D02

Additional information

Funding

The first author is financially supported by the University Grant Commission, India. The second author is partially funded by MATRICS grant, project no. MTR/2020/000635, from Science and Engineering Research Board (SERB), India.