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arXiv · 2105.05007

Closed Neighborhood Ideals of Finite Simple Graphs

Jacob Honeycutt·Keri Sather-Wagstaff
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Abstract

We investigate Sharifan and Moradi's closed neighborhood ideal of a finite simple graph, which is a square-free monomial ideal in a polynomial ring over a field. We explicitly describe the minimal irreducible decompositions of these ideals. We also characterize the trees whose closed neighborhood ideals are Cohen-Macaulay; in particular, this property for closed neighborhood ideals of trees is characteristic independent.

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Jacob Honeycutt, Keri Sather-Wagstaff. 2021-05-11. Closed Neighborhood Ideals of Finite Simple Graphs. https://arxiv.org/abs/2105.05007

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