{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T01:41:01Z","timestamp":1782870061162,"version":"3.54.5"},"reference-count":20,"publisher":"Oxford University Press (OUP)","issue":"12","license":[{"start":{"date-parts":[[2022,10,25]],"date-time":"2022-10-25T00:00:00Z","timestamp":1666656000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2023,12,14]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Let $ G $ be a graph. A set $ S $ of vertices in $ G $ is a disjunctive total dominating set of $ G $ if every vertex is adjacent to a vertex of $ S $ or has at least two vertices in $ S $ at distance two from it. The disjunctive total domination number, $ \\gamma _t^d(G) $, is the minimum cardinality of such a set. In this paper, we determine disjunctive total domination number of Harary graph $ H_{k,n} $ for all $ k $ and $ n $.<\/jats:p>","DOI":"10.1093\/comjnl\/bxac142","type":"journal-article","created":{"date-parts":[[2022,10,25]],"date-time":"2022-10-25T17:15:02Z","timestamp":1666718102000},"page":"2990-2999","source":"Crossref","is-referenced-by-count":3,"title":["Disjunctive Total Domination In Harary Graphs"],"prefix":"10.1093","volume":"66","author":[{"given":"Canan","family":"\u00c7ift\u00e7i","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Arts and Sciences, Ordu University , 52200, Ordu, Turkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Vecd\u0307","family":"Ayta\u00e7","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Faculty of Engineering, Ege University , 35100, Izmir, Turkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2022,10,25]]},"reference":[{"key":"2023121811454935900_ref1","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes","year":"1998"},{"issue":"3","key":"2023121811454935900_ref2","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1002\/net.3230070305","article-title":"Towards a theory of domination in graphs","volume":"7","author":"Cockayne","year":"1977","journal-title":"Networks"},{"issue":"3","key":"2023121811454935900_ref3","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1002\/net.3230100304","article-title":"Total domination in graphs","volume":"10","author":"Cockayne","year":"1980","journal-title":"Networks"},{"issue":"4","key":"2023121811454935900_ref4","doi-asserted-by":"crossref","first-page":"547","DOI":"10.2989\/16073606.2014.894688","article-title":"The disjunctive domination number of a graph","volume":"37","author":"Goddard","year":"2014","journal-title":"Quaestiones Mathematicae"},{"issue":"2","key":"2023121811454935900_ref5","first-page":"139","article-title":"Exponential domination and bondage numbers in some graceful cyclic structure","volume":"17","author":"Ayta\u00e7","year":"2017","journal-title":"Nonlinear Dynamics and Systems Theory"},{"issue":"3","key":"2023121811454935900_ref6","doi-asserted-by":"crossref","first-page":"11","DOI":"10.32513\/tbilisi\/1601344895","article-title":"Semitotal domination of Harary graphs","volume":"13","author":"Kartal","year":"2020","journal-title":"Tbilisi Mathematical Journal"},{"issue":"2","key":"2023121811454935900_ref7","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1134\/S0001434620010228","article-title":"Porous exponential domination in Harary graphs","volume":"107","author":"\u00c7ift\u00e7i","year":"2020","journal-title":"Mathematical Notes"},{"issue":"3","key":"2023121811454935900_ref8","doi-asserted-by":"crossref","first-page":"1090","DOI":"10.1007\/s10878-014-9811-4","article-title":"Disjunctive total domination in graphs","volume":"31","author":"Henning","year":"2016","journal-title":"Journal of Combinatorial Optimization"},{"issue":"1","key":"2023121811454935900_ref9","doi-asserted-by":"crossref","first-page":"153","DOI":"10.7151\/dmgt.1854","article-title":"Bounds on the disjunctive total domination number of a tree","volume":"36","author":"Henning","year":"2016","journal-title":"Discussiones Mathematicae Graph Theory"},{"key":"2023121811454935900_ref10","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1007\/978-3-319-26626-8_48","volume-title":"Combinatorial Optimization and Applications","author":"Yi","year":"2015"},{"issue":"2","key":"2023121811454935900_ref11","doi-asserted-by":"crossref","first-page":"185","DOI":"10.33401\/fujma.790046","article-title":"Disjunctive total domination of some shadow distance graphs","volume":"3","author":"\u00c7ift\u00e7i","year":"2020","journal-title":"Fundamental Journal of Mathematics and Applications"},{"key":"2023121811454935900_ref12","doi-asserted-by":"crossref","first-page":"15","DOI":"10.3233\/FI-2020-1928","article-title":"Disjunctive total domination subdivision number of graphs","volume":"174","author":"\u00c7ift\u00e7i","year":"2020","journal-title":"Fundamenta Informaticae"},{"issue":"9","key":"2023121811454935900_ref13","doi-asserted-by":"crossref","first-page":"7722","DOI":"10.1002\/mma.6615","article-title":"Disjunctive total domination stability in graphs","volume":"44","author":"\u00c7ift\u00e7i","year":"2021","journal-title":"Mathematical Methods in the Applied Sciences"},{"issue":"7","key":"2023121811454935900_ref14","doi-asserted-by":"crossref","first-page":"1142","DOI":"10.1073\/pnas.48.7.1142","article-title":"The maximum connectivity of a graph","volume":"48","author":"Harary","year":"1962","journal-title":"Proc. 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