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.
@article{arxiv.1802.06316,
title = {Projective dimension and regularity of edge ideal of some weighted oriented graphs},
author = {Guangjun Zhu and Li Xu and Hong Wang and Zhongming Tang},
journal= {arXiv preprint arXiv:1802.06316},
year = {2018}
}