{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,10]],"date-time":"2025-11-10T20:57:33Z","timestamp":1762808253546},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2014,9]]},"abstract":"<jats:p> A set of vertices of a graph whose removal leaves an acyclic graph is called a decycling set of the graph. The minimum size of a decycling set of a graph G is referred to as the decycling number of G, denoted by \u2207(G). In this paper, we study the decycling number of the Cartesian product of two paths, \u2207(P<jats:sub>m<\/jats:sub>\u25a1P<jats:sub>n<\/jats:sub>), and obtain several new results. Mainly, we prove that [Formula: see text]. Moreover, we obtain the exact value of \u2207(P<jats:sub>m<\/jats:sub>\u25a1P<jats:sub>n<\/jats:sub>) for some classes (modulo 6) of pairs (m, n). <\/jats:p>","DOI":"10.1142\/s1793830914500335","type":"journal-article","created":{"date-parts":[[2014,2,20]],"date-time":"2014-02-20T05:48:52Z","timestamp":1392875332000},"page":"1450033","source":"Crossref","is-referenced-by-count":1,"title":["The decycling number of $P_{m} \\square P_{n}^{\\ast}$"],"prefix":"10.1142","volume":"06","author":[{"given":"Min-Yun","family":"Lien","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 30010, Taiwan"}]},{"given":"Hung-Lin","family":"Fu","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 30010, Taiwan"}]},{"given":"Chie-Huai","family":"Shih","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, National Chiao Tung University, Hsinchu, 30010, Taiwan"}]}],"member":"219","published-online":{"date-parts":[[2014,6,16]]},"reference":[{"key":"rf1","first-page":"129","volume":"59","author":"Bau S.","journal-title":"Util. Math."},{"key":"rf2","first-page":"285","volume":"25","author":"Bau S.","journal-title":"Australas. J. Combin."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0118(199705)25:1<59::AID-JGT4>3.0.CO;2-H"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(02)00266-1"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-3023-4_4"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(00)00127-7"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(94)00133-2"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0020-0190(98)00039-8"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.08.007"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-003-0529-9"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1137\/S089548010444016X"},{"key":"rf12","first-page":"155","volume":"35","author":"Punnim N.","journal-title":"Australas. J. Combin."},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1002\/net.20067"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2003.11.001"},{"key":"rf15","volume-title":"Introduction to Graph Theory","author":"West D. B.","year":"2001"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.10.021"},{"key":"rf17","first-page":"3","volume":"52","author":"Xu X.","journal-title":"Australas. J. Combin."},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2006.09.010"},{"key":"rf19","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.11650\/twjm\/1500406287","volume":"15","author":"Xu X.","journal-title":"Taiwaness J. Math."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830914500335","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:15:48Z","timestamp":1565111748000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830914500335"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6,16]]},"references-count":19,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2014,6,16]]},"published-print":{"date-parts":[[2014,9]]}},"alternative-id":["10.1142\/S1793830914500335"],"URL":"https:\/\/doi.org\/10.1142\/s1793830914500335","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6,16]]}}}