@article{614530823b6848319822a939c503ad8d,
title = "Algebraic invariants of weighted oriented graphs",
abstract = "Let D be a weighted oriented graph and let I(D) be its edge ideal in a polynomial ring R. We give the formula of Castelnuovo–Mumford regularity of R/ I(D) when D is a weighted oriented path or cycle such that edges of D are oriented in one direction. Additionally, we compute the projective dimension for this class of graphs.",
author = "Selvi Kara and Jennifer Biermann and Lin, {Kuei Nuan} and Augustine O{\textquoteright}Keefe",
note = "Funding Information: This material is based upon work supported by the National Security Agency under Grant No. H98230-19-1-0119, The Lyda Hill Foundation, The McGovern Foundation, and Microsoft Research, while the authors were in residence at the Mathematical Sciences Research Institute in Berkeley, California, during the summer of 2019. The authors would like to thank Mathematical Sciences Research Institute for their support and hospitality. The authors are grateful for the reviewer{\textquoteright}s careful reading and constructive suggestions to improve this manuscript. Publisher Copyright: {\textcopyright} 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.",
year = "2022",
month = mar,
doi = "10.1007/s10801-021-01058-2",
language = "English (US)",
volume = "55",
pages = "461--491",
journal = "Journal of Algebraic Combinatorics",
issn = "0925-9899",
publisher = "Springer Netherlands",
number = "2",
}