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arXiv · 2107.06228

Dominating ideals and closed neighborhood ideals of graphs

Mehrdad Nasernejad·Ayesha Asloob Qureshi·Somayeh Bandari·Asli Musapasaouglu
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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.

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Mehrdad Nasernejad, Ayesha Asloob Qureshi, Somayeh Bandari, Asli Musapasaouglu. 2021-07-13. Dominating ideals and closed neighborhood ideals of graphs. https://arxiv.org/abs/2107.06228

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