{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T02:36:17Z","timestamp":1774578977589,"version":"3.50.1"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2020,4]]},"abstract":"<jats:p> In this paper, a new model of domination in graphs called the pitchfork domination is introduced. Let [Formula: see text] be a finite, simple and undirected graph without isolated vertices, a subset [Formula: see text] of [Formula: see text] is a pitchfork dominating set if every vertex [Formula: see text] dominates at least [Formula: see text] and at most [Formula: see text] vertices of [Formula: see text], where [Formula: see text] and [Formula: see text] are non-negative integers. The domination number of [Formula: see text], denotes [Formula: see text] is a minimum cardinality over all pitchfork dominating sets in [Formula: see text]. In this work, pitchfork domination when [Formula: see text] and [Formula: see text] is studied. Some bounds on [Formula: see text] related to the order, size, minimum degree, maximum degree of a graph and some properties are given. Pitchfork domination is determined for some known and new modified graphs. Finally, a question has been answered and discussed that; does every finite, simple and undirected graph [Formula: see text] without isolated vertices have a pitchfork domination or not? <\/jats:p>","DOI":"10.1142\/s1793830920500251","type":"journal-article","created":{"date-parts":[[2020,1,30]],"date-time":"2020-01-30T07:51:14Z","timestamp":1580370674000},"page":"2050025","source":"Crossref","is-referenced-by-count":31,"title":["Pitchfork domination in graphs"],"prefix":"10.1142","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1125-4439","authenticated-orcid":false,"given":"Manal N.","family":"Al-Harere","sequence":"first","affiliation":[{"name":"Department of Applied Sciences, University of Technology, Baghdad, Iraq"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0620-4576","authenticated-orcid":false,"given":"Mohammed A.","family":"Abdlhusein","sequence":"additional","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"}]}],"member":"219","published-online":{"date-parts":[[2020,3,9]]},"reference":[{"key":"S1793830920500251BIB001","doi-asserted-by":"publisher","DOI":"10.22401\/ANJS.00.2.18"},{"key":"S1793830920500251BIB002","doi-asserted-by":"publisher","DOI":"10.1063\/1.5097810"},{"key":"S1793830920500251BIB003","doi-asserted-by":"publisher","DOI":"10.21123\/bsj.15.4.466-471"},{"key":"S1793830920500251BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2013.06.012"},{"key":"S1793830920500251BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-017-1869-1"},{"key":"S1793830920500251BIB006","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"key":"S1793830920500251BIB007","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. 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