Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Closed Neighborhood Ideals of Finite Simple Graphs   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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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
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The categories of this paper are: econ