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

被引：5

作者：

Zhu, Guangjun ^{[1
]}

Wang, Hong ^{[1
]}

Xu, Li ^{[1
]}

Zhang, Jiaqi ^{[1
]}

机构：

[1] Soochow Univ, Sch Math Sci, Suzhou 215006, Jiangsu, Peoples R China

来源：

ALGEBRA COLLOQUIUM | 2021年 / 28卷 / 02期

基金：

中国国家自然科学基金;

关键词：

projective dimension; regularity; edge ideal; cyclic graph with a common vertex; cyclic graph with a common edge; PROJECTIVE DIMENSION; REGULARITY;

D O I：

10.1142/S1005386721000201

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：253 / 268

页数：16

共 22 条

[1] Graded Betti numbers of path ideals of cycles and lines
Alilooee, A.
Faridi, S.
[J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2018, 17 (01)
[2] BANGJENSEN J, 2006, DIGRAPHS THEORY ALGO
[3] Bondy J.A., 2008, GTM
[4] Path ideals of rooted trees and their graded Betti numbers
Bouchat, Rachelle R.
Ha, Huy Tai
O'Keefe, Augustine
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 2011, 118 (08) : 2411 - 2425
[5] Bruns W., 1998, COHEN MACAULAY RINGS
[6] CoCoATeam, CoCoA: A system for doing Computations in Commutative Algebra
[7] Dao HL, 2015, P AM MATH SOC, V143, P555
[8] Bounds on the regularity and projective dimension of ideals associated to graphs
Dao, Hailong
Huneke, Craig
Schweig, Jay
[J]. JOURNAL OF ALGEBRAIC COMBINATORICS, 2013, 38 (01) : 37 - 55
[9] SPLITTINGS OF MONOMIAL IDEALS
Francisco, Christopher A.
Ha, Huy Tai
Van Tuyl, Adam
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 137 (10) : 3271 - 3282
[10] Gimenez P., 2018, Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics, P491

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