activity
20232026
collaborators

13 papers

math.AC2026

Depth of powers of the edge ideal of an increasing weighted path

Jiaxin Li, Dancheng Lu, Thanh Vu +1

We provide exact formulas for the depth of the quotient ring of powers of the edge ideal of an increasing weighted path.

math.AC2025

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

Jiaxin Li, Thanh Vu, Guangjun Zhu

We compute the depth of powers of edge ideals of integrally closed edge-weighted paths.

math.AC2025

Depth and regularity of powers of edge ideals of edge-weighted trees

Truong Thi Hien, Jiaxin Li, Tran Nam Trung +1

For an increasing weighted tree , we obtain an asymptotic value and a sharp bound on the index stability of the depth function of its edge ideal . Moreover, if i…

math.AC2025

Cohen-Macaulayness of Powers of Edge Ideals of Weighted Oriented Graphs

Truong Thi Hien, Jiaxin Li, Tran Nam Trung +1

For the edge ideal $I(\D)$ of a weighted oriented graph $\D$, we prove that its symbolic powers $I(\D)^{(t)}$ are Cohen-Macaulay for all if and only if the underlyin…

math.AC2025

Associated primes of powers of edge ideals of edge-weighted trees

Jiaxin Li, Tran Nam Trung, Guangjun Zhu

In this paper, we give a complete description of the associated primes of each power of the edge ideal of an increasing weighted tree.

math.AC2025

The regularity of monomial ideals and their integral closures

Yijun Cui, Cheng Gong, Guangjun Zhu

Let be a monomial ideal in a polynomial ring over a field with or , and let be its integral closure. We will show that $\text{…

math.AC2025

Cohen-Macaulayness of powers of edge ideals of edge-weighted graphs

Jiaxin Li, Tran Nam Trung, Guangjun Zhu

In this paper, we characterize the Cohen-Macaulayness of the second power of the weighted edge ideal when the underlying graph is a very well-covered graph.…

math.AC2025

Depth of powers of edge ideals of edge-weighted integrally closed cycles

Guangjun Zhu, Jiaxin Li, Yijun Cui +1

This paper gives some exact formulas for the depth of powers of the edge ideal of an edge-weighted integrally closed cycle.

math.AC2024

Normal edge ideals of edge-weighted graphs

Thanh Vu, Guangjun Zhu

We classify all normal edge ideals of edge-weighted graphs.

math.AC2024

Regularity of powers of edge ideals of edge-weighted integrally closed cycles

Guangjun Zhu, Yijun Cui, Jiaxin Li +1

This paper gives exact formulas for the regularity of powers of edge ideals of an edge-weighted integrally closed cycle.

math.AC2024

Regularity of integral closures of edge ideals of weighted oriented graphs

Nguyen Cong Minh, Thanh Vu, Guangjun Zhu

We prove that the regularity cannot increase when taking the integral closure for edge ideals of arbitrary weighted oriented graphs.

math.AC2024

Powers of edge ideals of edge-weighted trees

Jiaxin Li, Guangjun Zhu, Shiya Duan

This paper gives exact formulas for the regularity of edge ideals of edge-weighted integrally closed trees. In addition, we provide some linear upper bounds on the regularity of po…

math.AC2023

The operation and operation of fan graphs

Guangjun Zhu, Yijun Cui, Yulong Yang +1

Let be a finite simple graph on the vertex set and let denote its edge ideal in the polynomial ring . In this paper, we compute the depth and the C…