Projective dimension and regularity of edge ideals of some vertex-weighted oriented $m$-partite graphs

Guangjun Zhu; Hong Wang; Li Xu; Jiaqi Zhang

Projective dimension and regularity of edge ideals of some vertex-weighted oriented $m$-partite graphs

Commutative Algebra 2019-06-04 v1

Authors: Guangjun Zhu , Hong Wang , Li Xu , Jiaqi Zhang

Abstract

In this paper we provide some exact formulas for the projective dimension and the regularity of edge ideals associated to three special types of vertex-weighted oriented $m$ -partite graphs. These formulas are functions of the weight and number of vertices. We also give some examples to show that these formulas are related to direction selection and the weight of vertices.

Keywords

projective dimension regularity edge ideals vertex-weighted oriented m-partite graphs commutative algebra

Cite

@article{arxiv.1904.04682,
  title  = {Projective dimension and regularity of edge ideals of some vertex-weighted oriented $m$-partite graphs},
  author = {Guangjun Zhu and Hong Wang and Li Xu and Jiaqi Zhang},
  journal= {arXiv preprint arXiv:1904.04682},
  year   = {2019}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1904.03019, arXiv:1904.02305, arXiv:1802.06316

Projective dimension and regularity of edge ideals of some vertex-weighted oriented $m$-partite graphs

Abstract

Keywords

Cite

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