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

Published 11 Jul 2025 in math.AC and math.CO | (2507.08777v1)

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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