Dominating ideals and closed neighborhood ideals of graphs

2021/07/13 by Mehrdad Nasernejad, Ayesha Asloob Qureshı, Nasernejad, Mehrdad +5 · 4 citations
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2107.06228

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.

Cited by

• Barile-Macchia Resolutions and the closed neighborhood ideal
• Criteria for the presence of the maximal ideal in the set of associated primes
• Demotions of ideals in commutative rings with applications to normally torsion-freeness
• Associated primes of the second power of closed neighborhood ideals of graphs

Related

• Algebraic implications of neighborhood hypergraphs and their transversal hypergraphs
• Normality and associated primes of Closed neighborhood ideals and dominating ideals
• Almost normally torsionfree ideals
• Open Neighborhood Ideals of Well Totally Dominated Trees are Cohen-Macaulay
• Closed Neighborhood Ideals of Finite Simple Graphs