English

Closed Neighborhood Ideals of Finite Simple Graphs

Commutative Algebra 2021-06-17 v2

Abstract

We investigate Sharifan and Moradi's closed neighborhood ideal of a finite simple graph, which is a square-free monomial ideal in a polynomial ring over a field. We explicitly describe the minimal irreducible decompositions of these ideals. We also characterize the trees whose closed neighborhood ideals are Cohen-Macaulay; in particular, this property for closed neighborhood ideals of trees is characteristic independent.

Keywords

Cite

@article{arxiv.2105.05007,
  title  = {Closed Neighborhood Ideals of Finite Simple Graphs},
  author = {Jacob Honeycutt and Keri Sather-Wagstaff},
  journal= {arXiv preprint arXiv:2105.05007},
  year   = {2021}
}

Comments

7 pages; v.2 update author name and add references, especially to arXiv:2003.04841