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arXiv · 2507.08777

Associated primes of the second power of closed neighborhood ideals of graphs

Ha Thi Thu Hien·Thanh Vu
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Abstract

We study simple graphs for which the maximal homogeneous ideal is an associated prime of the second power of their closed neighborhood ideals. In particular, we show that such graphs must have diameter at most $6$, and that those with diameter $2$ must be vertex diameter-$2$-critical.

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Ha Thi Thu Hien, Thanh Vu. 2025-07-11. Associated primes of the second power of closed neighborhood ideals of graphs. https://arxiv.org/abs/2507.08777

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