Crew, LoganSpirkl, Sophie2022-08-122022-08-122020-10https://doi.org/10.1016/j.ejc.2020.103143http://hdl.handle.net/10012/18526The final publication is available at Elsevier via https://doi.org/10.1016/j.ejc.2020.103143 © 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/We extend the definition of the chromatic symmetric function XG to include graphs G with a vertex-weight function w : V (G) --> N. We show how this provides the chromatic symmetric function with a natural deletion-contraction relation analogous to that of the chromatic polynomial. Using this relation we derive new properties of the chromatic symmetric function, and we give alternate proofs of many fundamental properties of XG.enAttribution-NonCommercial-NoDerivatives 4.0 Internationalsymmetric functionschromatic symmetric functionArticle