{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T02:34:46Z","timestamp":1774578886192,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,8]]},"abstract":"<jats:p> New two domination types are introduced in this paper. Let [Formula: see text] be a finite, simple, and undirected graph without isolated vertex. A dominating subset [Formula: see text] is a total pitchfork dominating set if [Formula: see text] for every [Formula: see text] and [Formula: see text] has no isolated vertex. [Formula: see text] is an inverse total pitchfork dominating set if [Formula: see text] is a total pitchfork dominating set of [Formula: see text]. The cardinality of a minimum (inverse) total pitchfork dominating set is the (inverse) total pitchfork domination number ([Formula: see text]) [Formula: see text]. Some properties and bounds are studied associated with maximum degree, minimum degree, order, and size of the graph. These modified domination parameters are applied on some standard and complement graphs. <\/jats:p>","DOI":"10.1142\/s1793830921500385","type":"journal-article","created":{"date-parts":[[2020,10,15]],"date-time":"2020-10-15T07:50:34Z","timestamp":1602748234000},"page":"2150038","source":"Crossref","is-referenced-by-count":16,"title":["Total pitchfork domination and its inverse in graphs"],"prefix":"10.1142","volume":"13","author":[{"given":"Mohammed A.","family":"Abdlhusein","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Education for Pure Sciences (Ibn Al-Haitham), Baghdad University, Baghdad, Iraq"},{"name":"Department of Mathematics, College of Education for Pure Sciences, Thi-Qar University, Thi-Qar, Iraq"}]},{"given":"Manal N.","family":"Al-Harere","sequence":"additional","affiliation":[{"name":"Department of Applied Sciences, University of Technology, Baghdad, Iraq"}]}],"member":"219","published-online":{"date-parts":[[2020,11,27]]},"reference":[{"issue":"1","key":"S1793830921500385BIB002","first-page":"13","volume":"9","author":"Abdlhusein M. A.","year":"2020","journal-title":"Proc. Institute Appl. Math."},{"key":"S1793830921500385BIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830920500251"},{"key":"S1793830921500385BIB006","doi-asserted-by":"publisher","DOI":"10.1063\/1.5097810"},{"key":"S1793830921500385BIB007","doi-asserted-by":"publisher","DOI":"10.21123\/bsj.15.4.466-471"},{"key":"S1793830921500385BIB008","doi-asserted-by":"publisher","DOI":"10.5269\/bspm.v38i7.44282"},{"key":"S1793830921500385BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-017-1869-1"},{"key":"S1793830921500385BIB011","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"S1793830921500385BIB012","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"},{"key":"S1793830921500385BIB013","volume-title":"Domination in Graphs-Advanced Topics","author":"Haynes T. W.","year":"1998"},{"key":"S1793830921500385BIB014","volume-title":"Third Int. Conf. Sci. (ICMS2019)","volume":"2183","author":"Jabor A. A."},{"key":"S1793830921500385BIB015","doi-asserted-by":"publisher","DOI":"10.1090\/coll\/038"},{"key":"S1793830921500385BIB016","doi-asserted-by":"publisher","DOI":"10.1088\/1742-6596\/1591\/1\/012054"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921500385","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,12]],"date-time":"2021-07-12T09:04:18Z","timestamp":1626080658000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830921500385"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,11,27]]},"references-count":12,"journal-issue":{"issue":"04","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["10.1142\/S1793830921500385"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921500385","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,11,27]]}}}