{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T17:51:55Z","timestamp":1777398715853,"version":"3.51.4"},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2021,5]]},"abstract":"<jats:p> Let [Formula: see text] be a weighted oriented graph with the underlying graph [Formula: see text] when vertices with non-trivial weights are sinks and [Formula: see text] be the edge ideals corresponding to [Formula: see text] and [Formula: see text] respectively. We give an explicit description of the symbolic powers of [Formula: see text] using the concept of strong vertex covers. We show that the ordinary and symbolic powers of [Formula: see text] and [Formula: see text] behave in a similar way. We provide a description for symbolic powers and Waldschmidt constant of [Formula: see text] for certain classes of weighted oriented graphs. When [Formula: see text] is a weighted oriented odd cycle, we compute [Formula: see text] and prove [Formula: see text] and show that equality holds when there is only one vertex with non-trivial weight. <\/jats:p>","DOI":"10.1142\/s0218196721500260","type":"journal-article","created":{"date-parts":[[2021,3,23]],"date-time":"2021-03-23T04:15:31Z","timestamp":1616472931000},"page":"533-549","source":"Crossref","is-referenced-by-count":12,"title":["Symbolic powers in weighted oriented graphs"],"prefix":"10.1142","volume":"31","author":[{"given":"Mousumi","family":"Mandal","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dipak","family":"Kumar Pradhan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology, Kharagpur 721302, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2021,3,22]]},"reference":[{"key":"S0218196721500260BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s10801-016-0693-7"},{"key":"S0218196721500260BIB003","doi-asserted-by":"publisher","DOI":"10.1090\/S1056-3911-09-00530-X"},{"key":"S0218196721500260BIB004","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498820501844"},{"key":"S0218196721500260BIB005","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091516000110"},{"key":"S0218196721500260BIB006","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2020.1769120"},{"issue":"1","key":"S0218196721500260BIB007","first-page":"141","volume":"48","author":"Gitler I.","year":"2007","journal-title":"Beitr\u00e4ge Algebra Geom."},{"key":"S0218196721500260BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.aim.2013.05.027"},{"key":"S0218196721500260BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2013.05.028"},{"key":"S0218196721500260BIB010","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-2012-045-3"},{"key":"S0218196721500260BIB011","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2020.1745221"},{"key":"S0218196721500260BIB012","doi-asserted-by":"publisher","DOI":"10.1142\/S0218196719500139"},{"key":"S0218196721500260BIB013","doi-asserted-by":"publisher","DOI":"10.1007\/s00209-015-1566-9"},{"key":"S0218196721500260BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498819501846"},{"key":"S0218196721500260BIB015","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2016.06.006"},{"key":"S0218196721500260BIB016","doi-asserted-by":"publisher","DOI":"10.37236\/8479"},{"key":"S0218196721500260BIB017","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1994.1192"},{"key":"S0218196721500260BIB018","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-29244-0"},{"key":"S0218196721500260BIB019","doi-asserted-by":"publisher","DOI":"10.1216\/RMJ-2019-49-4-1391"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196721500260","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,5,18]],"date-time":"2021-05-18T04:22:54Z","timestamp":1621311774000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196721500260"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,22]]},"references-count":18,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2021,5]]}},"alternative-id":["10.1142\/S0218196721500260"],"URL":"https:\/\/doi.org\/10.1142\/s0218196721500260","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,22]]}}}