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arXiv · 2308.06016

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

Shiya Duan·Guangjun Zhu·Yijun Cui·Jiaxin Li
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Abstract

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

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Shiya Duan, Guangjun Zhu, Yijun Cui, Jiaxin Li. 2023-08-11. Integral closure and normality of edge ideals of some edge-weighted graphs. https://arxiv.org/abs/2308.06016

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