Integral closure and normality of edge ideals of some edge-weighted graphs

2023/08/11 by Shiya Duan, Guangjun Zhu, Duan, Shiya +5 · 1 citation
Mathematics · Neuroscience · #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #Mind wandering and attention

paper · pdf · doi:10.48550/arxiv.2308.06016

Abstract

Let G_ω be an edge-weighted simple graph. In this paper, we give a complete characterization of the graph G_ω whose edge ideal I(G_ω) is integrally closed. We also show that if G_ω is an edge-weighted star graph, a path or a cycle, and I(G_ω) is integrally closed, then I(G_ω) is normal.

Cited by

• Depth of powers of integrally closed edge ideals of edge-weighted paths

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• Edge ideals of some edge-weighted graphs
• Regularity of integral closures of edge ideals of weighted oriented graphs
• Normal edge ideals of edge-weighted graphs
• Regularity of powers of edge ideals of edge-weighted integrally closed cycles
• Integral closure of small powers of edge ideals and their regularity