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

Shiya Duan

https://orcid.org/0009-0001-3237-9006

School of Mathematical Sciences, Soochow University, Suzhou, Jiangsu 215006, P. R. China

E-mail Address: 3136566920@qq.com

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Guangjun Zhu

https://orcid.org/0000-0002-7196-1090

School of Mathematical Sciences, Soochow University, Suzhou, Jiangsu 215006, P. R. China

E-mail Address: zhuguangjun@suda.edu.cn

Corresponding author.

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Yijun Cui

https://orcid.org/0000-0001-5716-6499

School of Mathematical Sciences, Soochow University, Suzhou, Jiangsu 215006, P. R. China

E-mail Address: 237546805@qq.com

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Jiaxin Li

https://orcid.org/0009-0002-4490-0361

School of Mathematical Sciences, Soochow University, Suzhou, Jiangsu 215006, P. R. China

E-mail Address: lijiaxinworking@163.com

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https://doi.org/10.1142/S0219498826500921Cited by:0 (Source: Crossref)

Abstract

This paper presents a complete characterization of an edge-weighted simple graph $G_{ω}$ $G_{ω}$ , whose edge ideal $I (G_{ω})$ $I (G_{ω})$ is integrally closed. Furthermore, it is demonstrated that if $I (G_{ω})$ $I (G_{ω})$ is integrally closed and $G_{ω}$ $G_{ω}$ is an edge-weighted star graph, path, or cycle, then $I (G_{ω})$ $I (G_{ω})$ is normal.