{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,19]],"date-time":"2024-09-19T15:35:27Z","timestamp":1726760127348},"reference-count":18,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2015,3]]},"abstract":"<jats:p> The zero forcing number, Z(G), of a graph G is the minimum cardinality of a set S of black vertices (whereas vertices in V(G)\\S are colored white) such that V(G) is turned black after finitely many applications of \"the color-change rule\": a white vertex is converted to a black vertex if it is the only white neighbor of a black vertex. Zero forcing number was introduced and used to bound the minimum rank of graphs by the \"AIM Minimum Rank-Special Graphs Work Group\". It is known that Z(G) \u2265 \u03b4(G), where \u03b4(G) is the minimum degree of G. We show that Z(G) \u2264 n - 3 if a connected graph G of order n has a connected complement graph [Formula: see text]. Further, we characterize a tree or a unicyclic graph G which satisfies either [Formula: see text] or [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830915500020","type":"journal-article","created":{"date-parts":[[2014,11,12]],"date-time":"2014-11-12T21:08:25Z","timestamp":1415826505000},"page":"1550002","source":"Crossref","is-referenced-by-count":6,"title":["On zero forcing number of graphs and their complements"],"prefix":"10.1142","volume":"07","author":[{"given":"Linda","family":"Eroh","sequence":"first","affiliation":[{"name":"University of Wisconsin Oshkosh, Oshkosh, WI 54901, USA"}]},{"given":"Cong X.","family":"Kang","sequence":"additional","affiliation":[{"name":"Texas A&amp;M University at Galveston, Galveston, TX 77553, USA"}]},{"given":"Eunjeong","family":"Yi","sequence":"additional","affiliation":[{"name":"Texas A&amp;M University at Galveston, Galveston, TX 77553, USA"}]}],"member":"219","published-online":{"date-parts":[[2015,2,2]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2007.10.009"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2010.03.008"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21637"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2008.04.038"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.99.100501"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1088\/1367-2630\/11\/10\/103019"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-218X(00)00198-0"},{"key":"rf8","volume-title":"Introduction to Graph Theory","author":"Chartrand G.","year":"2004"},{"key":"rf9","first-page":"57","volume":"64","author":"Chilakamarri K.","year":"2012","journal-title":"Bull. Inst. Combin. Appl."},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(81)90013-5"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2010.10.015"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2007.05.036"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2011.06.041"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2012.04.003"},{"key":"rf17","first-page":"9","volume":"67","author":"Kang C. X.","year":"2013","journal-title":"Bull. Inst. Combin. Appl."},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.2307\/2306658"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2011.05.012"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/41\/48\/482002"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830915500020","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:25:30Z","timestamp":1565137530000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830915500020"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,2]]},"references-count":18,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2015,2,2]]},"published-print":{"date-parts":[[2015,3]]}},"alternative-id":["10.1142\/S1793830915500020"],"URL":"https:\/\/doi.org\/10.1142\/s1793830915500020","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,2]]}}}