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arXiv · 2602.14163

On the closed neighborhood ideal of the square of the path graph

Anda Olteanu·Oana Olteanu
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Abstract

We consider the closed neighborhood ideal of square of the path graph and study some of its algebraic and homological invariants. We compute the height, the projective dimension and the Castelnuovo-Mumford regularity. We prove that these ideals are sequentially Cohen-Macaulay and characterize when they are Cohen-Macaulay.

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Anda Olteanu, Oana Olteanu. 2026-02-15. On the closed neighborhood ideal of the square of the path graph. https://arxiv.org/abs/2602.14163

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