This paper presents exact formulas for the regularity and depth of powers of edge ideals of an edge-weighted star graph. Additionally, we provide exact formulas for the regularity of powers of the edge ideal of an edge-weighted integrally closed path, as well as lower bounds on the depth of powers of such an edge ideal.
@article{arxiv.2401.02111,
title = {Edge ideals of some edge-weighted graphs},
author = {Guangjun Zhu and Shiya Duan and Yijun Cui and Jiaxin Li},
journal= {arXiv preprint arXiv:2401.02111},
year = {2024}
}