Dominating ideals and closed neighborhood ideals of graphs
Commutative Algebra
2022-06-17 v4 Combinatorics
Abstract
We study the closed neighborhood ideals and the dominating ideals of graphs, in particular, of trees and cycles. We prove that the closed neighborhood ideals and the dominating ideals of trees are normally torsion-free. The closed neighborhood ideals and the dominating ideals of cycles fail to be normally torsion-free. However, we prove that the closed neighborhood ideals of cycles admit the (strong) persistence property and the dominating ideals of cycles are nearly normally torsion-free.
Keywords
Cite
@article{arxiv.2107.06228,
title = {Dominating ideals and closed neighborhood ideals of graphs},
author = {Mehrdad Nasernejad and Ayesha Asloob Qureshi and Somayeh Bandari and Asli Musapasaouglu},
journal= {arXiv preprint arXiv:2107.06228},
year = {2022}
}
Comments
Accepted in the Mediterranean Journal of Mathematics Lemma 2.5, Corollary 2.6, Corollary 2.8, Lemma 2.18, Corollary 2.19, and Corollary 2.20. arXiv admin note: text overlap with arXiv:2106.10219