## “School of Mathematics”

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Paper   IPM / M / 16908
 School of Mathematics Title: Dominating ideals and closed neighborhood ideals of graphs Author(s): Mehrdad Nassernejad (A. Asloob Qureshi, S. Bandari, and A. Musapasaoglu) Status: To Appear Journal: Mediterr. J. Math. Supported by: IPM
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.