Work

Open Neighborhood Ideals of Well-Totally Dominated Trees are Cohen-Macaulay

Year: 2025

Type: preprint

Abstract: We introduce and investigate the open neighborhood ideal $\mathcal{N}(G)$ of a finite simple graph $G$. We describe the minimal primary decomposition of $\mathcal{N}(G)$ in terms of the minimal total dominating sets (TDSs) of $G$. Then we prove that the open neighborhood ideal of a tree is Cohen-Macaulay if and only if the tree is well-totally dominated (WTD) and calculate the Cohen-Macaulay type.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2510.19707

Authors: Lim, Jounglag, Gossell, James, Sather-Wagstaff, Keri Ann

Language: English

Topic: Commutative Algebra and Its Applications

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Clemson University

OpenAlex ID: W4416248335

Cites:

Cited by: 3

Related to: 10