Algebraic Properties of Edge Ideals of Some Vertex-Weighted Oriented Cyclic Graphs

• 作者: Hong Wang Guangjun Zhu Li Xu Jiaqi Zhang
• 来源期刊: 代数集刊（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 253-268
• 页数: 16页
• 语种: 英文
• DOI: 10.1142/S1005386721000201

摘要

We provide some exact formulas for the projective dimension and regularity of edge ideals associated to some vertex-weighted oriented cyclic graphs with a common vertex or edge.These formulas are functions in the weight of the vertices,and the numbers of edges and cycles.Some examples show that these formulas are related to direction selection and the assumption that w(x)≥2 for any vertex x cannot be dropped.