Projective dimension and regularity of edge ideal of some weighted oriented graphs
Guangjun Zhu, Li Xu, Hong Wang, Zhongming Tang
TL;DR
This paper derives exact formulas for the projective dimension and regularity of edge ideals in weighted rooted forests and oriented cycles, also providing formulas for their depth, advancing understanding of their algebraic properties.
Contribution
It introduces new exact formulas for algebraic invariants of edge ideals in specific classes of weighted oriented graphs, expanding current theoretical knowledge.
Findings
Exact formulas for projective dimension and regularity.
Formulas for the depth of these ideals.
Application to weighted rooted forests and oriented cycles.
Abstract
In this paper we provide some exact formulas for the projective dimension and the regularity of edge ideals associated to vertex weighted rooted forests and oriented cycles. As some consequences, we give some exact formulas for the depth of these ideals.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Polynomial and algebraic computation