{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,29]],"date-time":"2025-03-29T16:50:53Z","timestamp":1743267053586,"version":"3.37.3"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","funder":[{"DOI":"10.13039\/501100001843","name":"SERB","doi-asserted-by":"crossref","award":["MTR\/2020\/000429"],"award-info":[{"award-number":["MTR\/2020\/000429"]}],"id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,8]]},"abstract":"<jats:p> Let [Formula: see text] be a weighted oriented graph and [Formula: see text] be its edge ideal. We provide one method to find all the minimal generators of [Formula: see text], where [Formula: see text] is a maximal strong vertex cover of [Formula: see text] and [Formula: see text] is the intersections of irreducible ideals associated to the strong vertex covers contained in [Formula: see text]. If [Formula: see text] is an induced digraph of [Formula: see text], under a certain condition on the strong vertex covers of [Formula: see text] and [Formula: see text], we show that [Formula: see text] for some [Formula: see text] implies [Formula: see text]. We provide the necessary and sufficient condition for the equality of ordinary and symbolic powers of edge ideal of the union of two naturally oriented paths with a common sink vertex. We characterize all the maximal strong vertex covers of [Formula: see text] such that at most one edge is oriented into each of its vertices and [Formula: see text] if [Formula: see text] for all [Formula: see text]. Finally, if [Formula: see text] is a weighted rooted tree with the degree of root is [Formula: see text] and [Formula: see text] when [Formula: see text] for all [Formula: see text], we show that [Formula: see text] for all [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218196723500406","type":"journal-article","created":{"date-parts":[[2023,6,2]],"date-time":"2023-06-02T02:21:58Z","timestamp":1685672518000},"page":"927-951","source":"Crossref","is-referenced-by-count":2,"title":["Properties of symbolic powers of edge ideals of weighted oriented graphs"],"prefix":"10.1142","volume":"33","author":[{"given":"Mousumi","family":"Mandal","sequence":"first","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Kharagpur 721302, India"}]},{"given":"Dipak Kumar","family":"Pradhan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Indian Institute of Technology Kharagpur 721302, India"}]}],"member":"219","published-online":{"date-parts":[[2023,6,30]]},"reference":[{"issue":"4","key":"S0218196723500406BIB002","doi-asserted-by":"crossref","first-page":"1575","DOI":"10.1080\/00927872.2022.2139834","volume":"51","author":"Banerjee A.","year":"2023","journal-title":"Commun. Algebra"},{"issue":"1","key":"S0218196723500406BIB003","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1017\/S0013091516000110","volume":"60","author":"Cooper S.","year":"2017","journal-title":"Proc. Edinb. Math. Soc."},{"key":"S0218196723500406BIB004","series-title":"Springer Proceedings in Mathematics and Statistics","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/978-3-319-73639-6_13","volume-title":"Singularities and Foliations. Geometry, Topology and Applications","volume":"222","author":"Dao H.","year":"2018"},{"key":"S0218196723500406BIB005","first-page":"491","volume-title":"Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics","author":"Gimenez P.","year":"2018"},{"key":"S0218196723500406BIB007","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1007\/s00209-019-02323-8","volume":"294","author":"H\u00e0 H. T.","year":"2020","journal-title":"Math. Z."},{"issue":"3","key":"S0218196723500406BIB008","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1142\/S0218196721500260","volume":"31","author":"Mandal M.","year":"2021","journal-title":"Int. J. Algebra Comput."},{"key":"S0218196723500406BIB009","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/s10801-022-01118-1","volume":"56","author":"Mandal M.","year":"2022","journal-title":"J Algebra Comb."},{"key":"S0218196723500406BIB010","doi-asserted-by":"crossref","first-page":"105621","DOI":"10.1016\/j.jcta.2022.105621","volume":"190","author":"Minh N. C.","year":"2022","journal-title":"J. Combin. Theory Ser. A"},{"issue":"3","key":"S0218196723500406BIB011","doi-asserted-by":"crossref","first-page":"1","DOI":"10.37236\/8479","volume":"26","author":"Pitones Y.","year":"2019","journal-title":"Electron. J. Combin."}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196723500406","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T15:59:44Z","timestamp":1691769584000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0218196723500406"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,6,30]]},"references-count":9,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2023,8]]}},"alternative-id":["10.1142\/S0218196723500406"],"URL":"https:\/\/doi.org\/10.1142\/s0218196723500406","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"type":"print","value":"0218-1967"},{"type":"electronic","value":"1793-6500"}],"subject":[],"published":{"date-parts":[[2023,6,30]]}}}